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## de la Llave, Rafael

Compute Distance To:
 Author ID: de-la-llave.rafael Published as: de la Llave, Rafael; de la Llave, R.; De la Llave, R.; De La Llave, Rafael; de La Llave, Rafael; De la Llave, Rafael; La Llave, Rafael De; De La Llave, R.; De la Lĺave, R. Homepage: http://people.math.gatech.edu/~rll6/ External Links: MGP · ORCID · ResearchGate · dblp
 Documents Indexed: 167 Publications since 1982, including 5 Books
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#### Serials

 13 Journal of Statistical Physics 13 Discrete and Continuous Dynamical Systems 11 Journal of Differential Equations 10 Nonlinearity 9 Communications in Mathematical Physics 8 SIAM Journal on Mathematical Analysis 8 SIAM Journal on Applied Dynamical Systems 7 Ergodic Theory and Dynamical Systems 5 Journal of Dynamics and Differential Equations 4 Advances in Mathematics 4 Physica D 4 Chaos 3 Transactions of the American Mathematical Society 3 Journal of Nonlinear Science 3 Journal of Physics A: Mathematical and Theoretical 2 Communications on Pure and Applied Mathematics 2 Journal of Mathematical Physics 2 Indiana University Mathematics Journal 2 Memoirs of the American Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 2 Mathematical Physics Electronic Journal 2 Regular and Chaotic Dynamics 2 Communications in Nonlinear Science and Numerical Simulation 2 Annales Henri Poincaré 2 Discrete and Continuous Dynamical Systems. Series B 2 Discrete and Continuous Dynamical Systems. Series S 1 American Mathematical Monthly 1 Archive for Rational Mechanics and Analysis 1 Mathematische Zeitschrift 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 The Journal of Geometric Analysis 1 Expositiones Mathematicae 1 Journal of Knot Theory and its Ramifications 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Experimental Mathematics 1 Mathematical Research Letters 1 Electronic Research Announcements of the American Mathematical Society 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Qualitative Theory of Dynamical Systems 1 La Gaceta de la Real Sociedad Matemática Española 1 Physical Review Letters 1 Communications on Pure and Applied Analysis 1 The IMA Volumes in Mathematics and its Applications 1 Proceedings of Symposia in Pure Mathematics 1 Networks and Heterogeneous Media 1 Journal of Modern Dynamics 1 Electronic Research Announcements in Mathematical Sciences
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#### Fields

 126 Dynamical systems and ergodic theory (37-XX) 54 Mechanics of particles and systems (70-XX) 23 Ordinary differential equations (34-XX) 19 Statistical mechanics, structure of matter (82-XX) 18 Partial differential equations (35-XX) 13 Numerical analysis (65-XX) 11 Global analysis, analysis on manifolds (58-XX) 8 Differential geometry (53-XX) 8 Fluid mechanics (76-XX) 7 Operator theory (47-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Functional analysis (46-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Functions of a complex variable (30-XX) 3 Difference and functional equations (39-XX) 3 Convex and discrete geometry (52-XX) 3 Manifolds and cell complexes (57-XX) 3 Probability theory and stochastic processes (60-XX) 3 Quantum theory (81-XX) 3 Biology and other natural sciences (92-XX) 2 Computer science (68-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

139 Publications have been cited 1,972 times in 836 Documents Cited by Year
Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation. Zbl 0603.58016
De la Llave, R.; Marco, J. M.; Moriyon, R.
1986
The parameterization method for invariant manifolds. I: Manifolds associated to non-resonant subspaces. Zbl 1034.37016
Cabré, Xavier; Fontich, Ernest; De La Llave, Rafael
2003
The parameterization method for invariant manifolds. III: Overview and applications. Zbl 1101.37019
Cabré, Xavier; Fontich, Ernest; de La Llave, Rafael
2005
A tutorial on KAM theory. Zbl 1055.37064
de la Llave, Rafael
2001
The parameterization method for invariant manifolds. II: Regularity with respect to parameters. Zbl 1034.37017
Cabré, Xavier; Fontich, Ernest; De La Llave, Rafael
2003
A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results. Zbl 1102.37017
Haro, A.; de la Llave, R.
2006
KAM theory without action-angle variables. Zbl 1067.37081
de la Llave, R.; González, A.; Jorba, À.; Villanueva, J.
2005
A geometric mechanism for diffusion in Hamiltonian systems overcoming in the large gap problem: Heuristics and rigorous verification on a model. Zbl 1090.37044
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2006
A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms. Zbl 1296.37048
Haro, À.; de la Llave, R.
2006
Relativistic stability of matter. I. Zbl 0602.58015
Fefferman, C.; de la Llave, R.
1987
A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity. Zbl 1210.37062
Haro, A.; de la Llave, R.
2007
A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of $$\mathbb{T}^2$$. Zbl 0952.70015
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2000
Planelike minimizers in periodic media. Zbl 1036.49040
Caffarelli, Luis A.; de la Llave, Rafael
2001
A KAM theory for conformally symplectic systems: efficient algorithms and their validation. Zbl 1345.37078
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael
2013
Geometric properties of the scattering map of a normally hyperbolic invariant manifold. Zbl 1131.37032
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2008
On squirt singularities in hydrodynamics. Zbl 1078.76018
Córdoba, Diego; Fefferman, Charles; de la Llave, Rafael
2004
Regularity of the composition operator in spaces of Hölder functions. Zbl 0956.47029
de la Llave, R.; Obaya, R.
1999
Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems. Zbl 0770.58029
de la Llave, R.
1992
Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108
Huguet, Gemma; de la Llave, Rafael
2013
A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification. Zbl 1209.37008
Calleja, Renato; de la Llave, Rafael
2010
Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions. Zbl 1209.37066
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick
2009
Computation of whiskered invariant tori and their associated manifolds: new fast algorithms. Zbl 1279.70004
Huguet, Gemma; de la Llave, Rafael; Sire, Yannick
2012
KAM theory and a partial justification of Greene’s criterion for nontwist maps. Zbl 1049.37032
Delshams, Amadeu; de la Llave, Rafael
2000
Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media. Zbl 1152.35038
de la Llave, Rafael; Valdinoci, Enrico
2007
On Irwin’s proof of the pseudostable manifold theorem. Zbl 0843.58100
de la Llave, Rafael; Wayne, C. Eugene
1995
A rigorous partial justification of Green’s criterion. Zbl 0892.58045
Falcolini, Corrado; de la Llave, R.
1992
Cohomology equations near hyperbolic points and geometric versions of Sternberg linearization theorem. Zbl 0918.53016
Banyaga, A.; de la Llave, R.; Wayne, C. E.
1996
Fast numerical computation of quasi-periodic equilibrium states in 1D statistical mechanics, including twist maps. Zbl 1183.37014
Calleja, Renato; de la Llave, Rafael
2009
Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems. Zbl 1230.37042
de la Llave, Rafael; Windsor, Alistair
2010
Invariants for smooth conjugacy of hyperbolic dynamical systems. II. Zbl 0673.58036
de la Llave, R.
1987
A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations. Zbl 1171.35372
de la Llave, Rafael; Valdinoci, Enrico
2009
Interfaces of ground states in Ising models with periodic coefficients. Zbl 1126.82305
Caffarelli, Luis A.; de la Llave, Rafael
2005
Topological methods in the instability problem of Hamiltonian systems. Zbl 1098.37056
Gidea, Marian; de la Llave, Rafael
2006
Ground states and critical points for Aubry-Mather theory in Statistical mechanics. Zbl 1196.82095
de la Llave, Rafael; Valdinoci, Enrico
2010
Whiskered and low dimensional tori in nearly integrable Hamiltonian systems. Zbl 1136.37349
de la Llave, R.; Wayne, C. E.
2004
Invariant manifolds associated to nonresonant spectral subspaces. Zbl 0965.37028
de la Llave, Rafael
1997
Ground states and critical points for generalized Frenkel-Kontorova models in $$\mathbb Z^d$$. Zbl 1206.82026
de la Llave, Rafael; Valdinoci, Enrico
2007
A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities. Zbl 1179.35340
de la Llave, Rafael
2009
Existence of ideal knots. Zbl 1028.57008
Gonzalez, O.; de la Llave, R.
2003
A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations. Zbl 1370.65046
Figueras, Jordi-Lluís; Gameiro, Marcio; Lessard, Jean-Philippe; de la Llave, Rafael
2017
A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. Zbl 1237.37040
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick
2009
Manifolds on the verge of a hyperbolicity breakdown. Zbl 1144.37352
Haro, À.; de la Llave, R.
2006
Lindstedt series for lower dimensional tori. Zbl 0961.37020
Jorba, Àngel; de la Llave, Rafael; Zou, Maorong
1999
On the Aubry-Mather theory in statistical mechanics. Zbl 0917.46070
Candel, A.; de la Llave, R.
1998
Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows. Zbl 1091.37018
Delshams, Amadeu; de La Llave, Rafael; Seara, Tere M.
2006
Construction of quasi-periodic solutions of delay differential equations via KAM techniques. Zbl 1184.34076
Li, Xuemei; de la Llave, Rafael
2009
Geometric approaches to the problem of instability in Hamiltonian systems: an informal presentation. Zbl 1144.37022
Delshams, Amadeu; Gidea, Marian; de la Llave, Rafael; Seara, Tere M.
2008
Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case. Zbl 1407.34094
He, Xiaolong; de la Llave, Rafael
2016
Aubry-Mather theory for functions on lattices. Zbl 0948.37015
Koch, Hans; de la Llave, Rafael; Radin, Charles
1997
Invariants for smooth conjugacy of hyperbolic dynamical systems. IV. Zbl 0673.58038
de la Llave, R.; Moriyón, R.
1988
Smooth dependence of thermodynamic limits of SRB-measures. Zbl 0956.37022
Jiang, Miaohua; de la Llave, Rafael
2000
Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors. Zbl 0892.58066
Falcolini, Corrado; de la Llave, R.
1992
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results. Zbl 1068.37043
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2003
Singularity theory for non-twist KAM tori. Zbl 1343.37043
González-Enríquez, A.; Haro, A.; de la Llave, R.
2014
The parameterization method for one-dimensional invariant manifolds of higher-dimensional parabolic fixed points. Zbl 1123.37011
Baldomá, Immaculada; Fontich, Ernest; de la Llave, Rafael; Martín, Pau
2007
Parameterization of invariant manifolds by reducibility for volume preserving and symplectic maps. Zbl 1252.32015
de la Llave, Rafael; Mireles James, Jason D.
2012
Accurate strategies for small divisor problems. Zbl 0739.58060
De la Llave, R.; Rana, David
1990
Construction of response functions in forced strongly dissipative systems. Zbl 1339.70040
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael
2013
Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices. Zbl 1351.37258
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick
2015
Variational methods for quasi-periodic solutions of partial differential equations. Zbl 0987.35015
de la Llave, Rafael
2000
Regularity of conjugacies between critical circle maps: an experimental study. Zbl 1116.37306
de la Llave, Rafael; Petrov, Nikola P.
2002
Computation of the breakdown of analyticity in statistical mechanics models: Numerical results and a renormalization group explanation. Zbl 1205.82067
Calleja, Renato; de la Llave, Rafael
2010
KAM theory for equilibrium states in 1-D statistical mechanics models. Zbl 1163.82002
de la Llave, Rafael
2008
Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion. Zbl 1355.37074
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2016
Symmetry for a Dirichlet-Neumann problem arising in water waves. Zbl 1202.35066
de la Llave, Rafael; Valdinoci, Enrico
2009
Accurate strategies for K. A. M. bounds and their implementation. Zbl 0747.65039
De la Llave, R.; Rana, D.
1991
Gravity waves on the surface of the sphere. Zbl 0844.76008
de la Llave, R.; Panayotaros, P.
1996
Regularity of critical invariant circles of the standard nontwist map. Zbl 1074.37026
Apte, A.; de la Llave, Rafael; Petrov, Nikola P.
2005
Analytic smoothing of geometric maps with applications to KAM theory. Zbl 1160.37024
González-Enríquez, A.; de la Llave, R.
2008
Local behavior near quasi-periodic solutions of conformally symplectic systems. Zbl 1274.70040
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael
2013
Critical points inside the gaps of ground state laminations for some models in statistical mechanics. Zbl 1132.82010
de la Llave, Rafael; Valdinoci, Enrico
2007
Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification. Zbl 1359.37121
Capiński, Maciej J.; Gidea, Marian; de la Llave, Rafael
2017
Numerical computations and computer assisted proofs of periodic orbits of the Kuramoto-Sivashinsky equation. Zbl 1370.65047
Figueras, Jordi-Lluís; de la Llave, Rafael
2017
Further rigidity properties of conformal Anosov systems. Zbl 1087.37024
De La Llave, R.
2004
KAM theory for quasi-periodic equilibria in one-dimensional quasi-periodic media. Zbl 1329.70046
Su, Xifeng; de la Llave, Rafael
2012
The obstruction criterion for non-existence of invariant circles and renormalization. Zbl 1190.37046
de la Llave, Rafael; Olvera, Arturo
2006
Barriers to transport and mixing in volume-preserving maps with nonzero flux. Zbl 1364.76066
Fox, Adam M.; de la Llave, Rafael
2015
An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations. Zbl 1407.37108
de la Llave, Rafael; Sire, Yannick
2019
Dynamical systems on lattices with decaying interaction. I: A functional analysis framework. Zbl 1213.37114
Fontich, Ernest; de la Llave, Rafael; Martín, Pau
2011
A computer-assisted study of global dynamic transitions for a noninvertible system. Zbl 1185.37174
Adomaitis, Raymond A.; Kevrekidis, Ioannis G.; de la Llave, Rafael
2007
Connecting orbits for compact infinite dimensional maps: computer assisted proofs of existence. Zbl 1343.37078
de la Llave, R.; Mireles James, J. D.
2016
Analytic regularity of solutions of Livsic’s cohomology equation and some applications to analytic conjugacy of hyperbolic dynamical systems. Zbl 0883.58024
de la Llave, R.
1997
Perturbations of geodesic flows by recurrent dynamics. Zbl 1362.37116
Gidea, Marian; de la Llave, Rafael
2017
Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds. Zbl 1213.37115
Fontich, Ernest; de la Llave, Rafael; Martín, Pau
2011
Linear response function for coupled hyperbolic attractors. Zbl 1084.37031
Jiang, Miaohua; de la Llave, Rafael
2006
Domains of analyticity and Lindstedt expansions of KAM tori in some dissipative perturbations of Hamiltonian systems. Zbl 1425.70037
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael
2017
Rates of convergence to equilibrium in the Prigogine-Misra-Courbage theory of irreversibility. Zbl 0511.60082
de la Llave, R.
1982
The analyticity breakdown for Frenkel-Kontorova models in quasi-periodic media: numerical explorations. Zbl 1266.82014
Blass, Timothy; de la Llave, Rafael
2013
Cohomology equations and commutators of germs of contact diffeomorphisms. Zbl 0671.58031
Banyaga, Augustin; de la Llave, Rafael; Wayne, C. Eugene
1989
Remarks on Sobolev regularity in Anosov systems. Zbl 1055.37030
de la Llave, Rafael
2001
Rigidity of higher-dimensional conformal Anosov systems. Zbl 1028.37021
de la Llave, Rafael
2002
Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. I: Finitely differentiable, hyperbolic case. Zbl 1384.34080
He, Xiaolong; de la Llave, Rafael
2017
Differentiability at the tip of Arnold tongues for Diophantine rotations: numerical studies and renormalization group explanations. Zbl 1226.82019
de la Llave, Rafael; Luque, Alejandro
2011
Convergence of differentiable functions on closed sets and remarks on the proofs of the “converse approximation lemmas”. Zbl 1223.26027
Li, Xuemei; de la Llave, Rafael
2010
Smooth dependence on parameters of solutions to cohomology equations over Anosov systems with applications to cohomology equations on diffeomorphism groups. Zbl 1222.37025
de la Llave, Rafael; Windsor, Alistair
2011
Time-dependent scattering theory for ODEs and applications to reaction dynamics. Zbl 1223.34119
Blazevski, Daniel; de la Llave, Rafael
2011
Fast iteration of cocycles over rotations and computation of hyperbolic bundles. Zbl 1308.70038
Huguet, Gemma; de la Llave, Rafael; Sire, Yannick
2013
Resonant equilibrium configurations in quasi-periodic media: perturbative expansions. Zbl 1382.70022
de la Llave, Rafael; Su, Xifeng; Zhang, Lei
2016
On the integrability of intermediate distributions for Anosov diffeomorphisms. Zbl 0824.58037
Jiang, M.; Pesin, Ya B.; de la Llave, R.
1995
KAM theory for quasi-periodic equilibria in 1D quasi-periodic media. II: Long-range interactions. Zbl 1339.70041
Su, Xifeng; de la Llave, Rafael
2012
A general mechanism of diffusion in Hamiltonian systems: qualitative results. Zbl 1437.37072
Gidea, Marian; La Llave, Rafael De; M-Seara, Tere
2020
Stable manifolds to bounded solutions in possibly ill-posed PDEs. Zbl 1448.35564
Cheng, Hongyu; de la Llave, Rafael
2020
Response solutions to quasi-periodically forced systems, even to possibly ill-posed PDEs, with strong dissipation and any frequency vectors. Zbl 1448.34117
Wang, Fenfen; de la Llave, Rafael
2020
A general mechanism of instability in Hamiltonian systems: skipping along a normally hyperbolic invariant manifold. Zbl 1454.37054
Gidea, Marian; de la Llave, Rafael; Seara, Tere M.
2020
An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations. Zbl 1407.37108
de la Llave, Rafael; Sire, Yannick
2019
Global Melnikov theory in Hamiltonian systems with general time-dependent perturbations. Zbl 1405.37065
Gidea, Marian; de la Llave, Rafael
2018
Uniform boundedness of iterates of analytic mappings implies linearization: a simple proof and extensions. Zbl 1402.32018
de la Llave, Rafael
2018
A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations. Zbl 1370.65046
Figueras, Jordi-Lluís; Gameiro, Marcio; Lessard, Jean-Philippe; de la Llave, Rafael
2017
Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification. Zbl 1359.37121
Capiński, Maciej J.; Gidea, Marian; de la Llave, Rafael
2017
Numerical computations and computer assisted proofs of periodic orbits of the Kuramoto-Sivashinsky equation. Zbl 1370.65047
Figueras, Jordi-Lluís; de la Llave, Rafael
2017
Perturbations of geodesic flows by recurrent dynamics. Zbl 1362.37116
Gidea, Marian; de la Llave, Rafael
2017
Domains of analyticity and Lindstedt expansions of KAM tori in some dissipative perturbations of Hamiltonian systems. Zbl 1425.70037
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael
2017
Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. I: Finitely differentiable, hyperbolic case. Zbl 1384.34080
He, Xiaolong; de la Llave, Rafael
2017
Resonant equilibrium configurations in quasi-periodic media: KAM theory. Zbl 1404.70057
de la Llave, Rafael; Su, Xifeng; Zhang, Lei
2017
A continuous family of equilibria in ferromagnetic media are ground states. Zbl 1376.82109
Su, Xifeng; de la Llave, Rafael
2017
On the global dynamics of an electroencephalographic mean field model of the neocortex. Zbl 1382.35318
2017
Simple proofs and extensions of a result of L. D. Pustylnikov on the nonautonomous Siegel theorem. Zbl 1385.37022
de la Llave, Rafael
2017
Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case. Zbl 1407.34094
He, Xiaolong; de la Llave, Rafael
2016
Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion. Zbl 1355.37074
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2016
Connecting orbits for compact infinite dimensional maps: computer assisted proofs of existence. Zbl 1343.37078
de la Llave, R.; Mireles James, J. D.
2016
Resonant equilibrium configurations in quasi-periodic media: perturbative expansions. Zbl 1382.70022
de la Llave, Rafael; Su, Xifeng; Zhang, Lei
2016
Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices. Zbl 1351.37258
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick
2015
Barriers to transport and mixing in volume-preserving maps with nonzero flux. Zbl 1364.76066
Fox, Adam M.; de la Llave, Rafael
2015
KAM tori and whiskered invariant tori for non-autonomous systems. Zbl 1364.37048
Canadell, Marta; de la Llave, Rafael
2015
Singularity theory for non-twist KAM tori. Zbl 1343.37043
González-Enríquez, A.; Haro, A.; de la Llave, R.
2014
Localized stable manifolds for whiskered tori in coupled map lattices with decaying interaction. Zbl 1304.37020
Blazevski, Daniel; de la Llave, Rafael
2014
An extension of Greene’s criterion for conformally symplectic systems and a partial justification. Zbl 1341.37031
Calleja, Renato C.; Celletti, Alessandra; Falcolini, Corrado; de la Llave, Rafael
2014
A KAM theory for conformally symplectic systems: efficient algorithms and their validation. Zbl 1345.37078
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael
2013
Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108
Huguet, Gemma; de la Llave, Rafael
2013
Construction of response functions in forced strongly dissipative systems. Zbl 1339.70040
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael
2013
Local behavior near quasi-periodic solutions of conformally symplectic systems. Zbl 1274.70040
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael
2013
The analyticity breakdown for Frenkel-Kontorova models in quasi-periodic media: numerical explorations. Zbl 1266.82014
Blass, Timothy; de la Llave, Rafael
2013
Fast iteration of cocycles over rotations and computation of hyperbolic bundles. Zbl 1308.70038
Huguet, Gemma; de la Llave, Rafael; Sire, Yannick
2013
Computation of whiskered invariant tori and their associated manifolds: new fast algorithms. Zbl 1279.70004
Huguet, Gemma; de la Llave, Rafael; Sire, Yannick
2012
Parameterization of invariant manifolds by reducibility for volume preserving and symplectic maps. Zbl 1252.32015
de la Llave, Rafael; Mireles James, Jason D.
2012
KAM theory for quasi-periodic equilibria in one-dimensional quasi-periodic media. Zbl 1329.70046
Su, Xifeng; de la Llave, Rafael
2012
KAM theory for quasi-periodic equilibria in 1D quasi-periodic media. II: Long-range interactions. Zbl 1339.70041
Su, Xifeng; de la Llave, Rafael
2012
Percival Lagrangian approach to the Aubry-Mather theory. Zbl 1337.70037
Su, Xifeng; de la Llave, Rafael
2012
Invariant manifolds for analytic difference equations. Zbl 1260.39008
de la Llave, Rafael; Lomelí, Héctor E.
2012
Tracing KAM tori in presymplectic dynamical systems. Zbl 1327.70014
Alishah, Hassan Najafi; de la Llave, Rafael
2012
Dynamical systems on lattices with decaying interaction. I: A functional analysis framework. Zbl 1213.37114
Fontich, Ernest; de la Llave, Rafael; Martín, Pau
2011
Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds. Zbl 1213.37115
Fontich, Ernest; de la Llave, Rafael; Martín, Pau
2011
Differentiability at the tip of Arnold tongues for Diophantine rotations: numerical studies and renormalization group explanations. Zbl 1226.82019
de la Llave, Rafael; Luque, Alejandro
2011
Smooth dependence on parameters of solutions to cohomology equations over Anosov systems with applications to cohomology equations on diffeomorphism groups. Zbl 1222.37025
de la Llave, Rafael; Windsor, Alistair
2011
Time-dependent scattering theory for ODEs and applications to reaction dynamics. Zbl 1223.34119
Blazevski, Daniel; de la Llave, Rafael
2011
Combination laws for scaling exponents and relation to the geometry of renormalization operators. Zbl 1242.82017
de la Llave, Rafael; Olvera, Arturo; Petrov, Nikola P.
2011
$$L^p$$-bounds for quasi-geostrophic equations via functional analysis. Zbl 1272.35165
de la Llave, Rafael; Valdinoci, Enrico
2011
A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification. Zbl 1209.37008
Calleja, Renato; de la Llave, Rafael
2010
Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems. Zbl 1230.37042
de la Llave, Rafael; Windsor, Alistair
2010
Ground states and critical points for Aubry-Mather theory in Statistical mechanics. Zbl 1196.82095
de la Llave, Rafael; Valdinoci, Enrico
2010
Computation of the breakdown of analyticity in statistical mechanics models: Numerical results and a renormalization group explanation. Zbl 1205.82067
Calleja, Renato; de la Llave, Rafael
2010
Convergence of differentiable functions on closed sets and remarks on the proofs of the “converse approximation lemmas”. Zbl 1223.26027
Li, Xuemei; de la Llave, Rafael
2010
Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions. Zbl 1209.37066
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick
2009
Fast numerical computation of quasi-periodic equilibrium states in 1D statistical mechanics, including twist maps. Zbl 1183.37014
Calleja, Renato; de la Llave, Rafael
2009
A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations. Zbl 1171.35372
de la Llave, Rafael; Valdinoci, Enrico
2009
A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities. Zbl 1179.35340
de la Llave, Rafael
2009
A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. Zbl 1237.37040
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick
2009
Construction of quasi-periodic solutions of delay differential equations via KAM techniques. Zbl 1184.34076
Li, Xuemei; de la Llave, Rafael
2009
Symmetry for a Dirichlet-Neumann problem arising in water waves. Zbl 1202.35066
de la Llave, Rafael; Valdinoci, Enrico
2009
An application of topological multiple recurrence to tiling. Zbl 1175.37023
de la Llave, Rafael; Windsor, A.
2009
Geometric properties of the scattering map of a normally hyperbolic invariant manifold. Zbl 1131.37032
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2008
Geometric approaches to the problem of instability in Hamiltonian systems: an informal presentation. Zbl 1144.37022
Delshams, Amadeu; Gidea, Marian; de la Llave, Rafael; Seara, Tere M.
2008
KAM theory for equilibrium states in 1-D statistical mechanics models. Zbl 1163.82002
de la Llave, Rafael
2008
Analytic smoothing of geometric maps with applications to KAM theory. Zbl 1160.37024
González-Enríquez, A.; de la Llave, R.
2008
Boundaries of Siegel disks: numerical studies of their dynamics and regularity. Zbl 1309.37045
de la Llave, Rafael; Petrov, Nikola P.
2008
Renormalization of arbitrary weak noises for one-dimensional critical dynamical systems: summary of results and numerical explorations. Zbl 1153.37022
Díaz-Espinosa, Oliver; de la Llave, Rafael
2008
A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity. Zbl 1210.37062
Haro, A.; de la Llave, R.
2007
Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media. Zbl 1152.35038
de la Llave, Rafael; Valdinoci, Enrico
2007
Ground states and critical points for generalized Frenkel-Kontorova models in $$\mathbb Z^d$$. Zbl 1206.82026
de la Llave, Rafael; Valdinoci, Enrico
2007
The parameterization method for one-dimensional invariant manifolds of higher-dimensional parabolic fixed points. Zbl 1123.37011
Baldomá, Immaculada; Fontich, Ernest; de la Llave, Rafael; Martín, Pau
2007
Critical points inside the gaps of ground state laminations for some models in statistical mechanics. Zbl 1132.82010
de la Llave, Rafael; Valdinoci, Enrico
2007
A computer-assisted study of global dynamic transitions for a noninvertible system. Zbl 1185.37174
Adomaitis, Raymond A.; Kevrekidis, Ioannis G.; de la Llave, Rafael
2007
Universal scalings of universal scaling exponents. Zbl 1114.37022
de la Llave, Rafael; Olvera, Arturo; Petrov, Nikola P.
2007
Renormalization and central limit theorem for critical dynamical systems with weak external noise. Zbl 1130.37022
Díaz-Espinosa, Oliver; de la Llave, Rafael
2007
A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results. Zbl 1102.37017
Haro, A.; de la Llave, R.
2006
A geometric mechanism for diffusion in Hamiltonian systems overcoming in the large gap problem: Heuristics and rigorous verification on a model. Zbl 1090.37044
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2006
A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms. Zbl 1296.37048
Haro, À.; de la Llave, R.
2006
Topological methods in the instability problem of Hamiltonian systems. Zbl 1098.37056
Gidea, Marian; de la Llave, Rafael
2006
Manifolds on the verge of a hyperbolicity breakdown. Zbl 1144.37352
Haro, À.; de la Llave, R.
2006
Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows. Zbl 1091.37018
Delshams, Amadeu; de La Llave, Rafael; Seara, Tere M.
2006
The obstruction criterion for non-existence of invariant circles and renormalization. Zbl 1190.37046
de la Llave, Rafael; Olvera, Arturo
2006
Linear response function for coupled hyperbolic attractors. Zbl 1084.37031
Jiang, Miaohua; de la Llave, Rafael
2006
Some recent progress in geometric methods in the instability problem in Hamiltonian mechanics. Zbl 1117.37031
de la Llave, Rafael
2006
Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems. Zbl 1080.37022
Fontich, Ernest; de la Llave, Rafael; Martín, Pau
2006
The parameterization method for invariant manifolds. III: Overview and applications. Zbl 1101.37019
Cabré, Xavier; Fontich, Ernest; de La Llave, Rafael
2005
KAM theory without action-angle variables. Zbl 1067.37081
de la Llave, R.; González, A.; Jorba, À.; Villanueva, J.
2005
Interfaces of ground states in Ising models with periodic coefficients. Zbl 1126.82305
Caffarelli, Luis A.; de la Llave, Rafael
2005
Regularity of critical invariant circles of the standard nontwist map. Zbl 1074.37026
Apte, A.; de la Llave, Rafael; Petrov, Nikola P.
2005
On the regularity of integrable conformal structures invariant under Anosov systems. Zbl 1072.37026
de la Llave, Rafael; Sadovskaya, Victoria
2005
On squirt singularities in hydrodynamics. Zbl 1078.76018
Córdoba, Diego; Fefferman, Charles; de la Llave, Rafael
2004
Whiskered and low dimensional tori in nearly integrable Hamiltonian systems. Zbl 1136.37349
de la Llave, R.; Wayne, C. E.
2004
Further rigidity properties of conformal Anosov systems. Zbl 1087.37024
De La Llave, R.
2004
The parameterization method for invariant manifolds. I: Manifolds associated to non-resonant subspaces. Zbl 1034.37016
Cabré, Xavier; Fontich, Ernest; De La Llave, Rafael
2003
The parameterization method for invariant manifolds. II: Regularity with respect to parameters. Zbl 1034.37017
Cabré, Xavier; Fontich, Ernest; De La Llave, Rafael
2003
Existence of ideal knots. Zbl 1028.57008
Gonzalez, O.; de la Llave, R.
2003
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results. Zbl 1068.37043
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M.
2003
Invariant manifolds associated to invariant subspaces without invariant complements: a graph transform approach. Zbl 1115.37019
de la Llave, R.
2003
Torus maps and the problem of a one-dimensional optical resonator with a quasiperiodically moving wall. Zbl 1027.78010
Petrov, Nikola P.; de la Llave, Rafael; Vano, John A.
2003
Regularity of conjugacies between critical circle maps: an experimental study. Zbl 1116.37306
de la Llave, Rafael; Petrov, Nikola P.
2002
Rigidity of higher-dimensional conformal Anosov systems. Zbl 1028.37021
de la Llave, Rafael
2002
...and 39 more Documents
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#### Cited by 852 Authors

 82 de la Llave, Rafael 29 Mireles-James, Jason D. 24 Valdinoci, Enrico 17 Haro, Àlex 16 Lessard, Jean-Philippe 15 Haller, George 14 Fontich, Ernest 13 Celletti, Alessandra 13 M-Seara, Tere 12 Calleja, Renato C. 12 Delshams, Amadeu 11 Gidea, Marian 11 Martín, Pau 11 Meiss, James D. 9 Braides, Andrea 9 Figueras, Jordi-Lluís 9 Gentile, Guido 9 Katok, Anatole B. 9 Luque, Alejandro 9 van den Berg, Jan Bouwe 9 Villanueva, Jordi 8 Kaloshin, Vadim Yu. 8 Koch, Hans-Friedrich 8 Rabinowitz, Paul Henry 8 Zgliczyński, Piotr 7 Bolotin, Sergeĭ Vladimirovich 7 Capinski, Maciej J. 7 Chae, Dongho 7 Falcolini, Corrado 7 Lieb, Elliott H. 7 Paternain, Gabriel Pedro 7 Qin, Wenxin 7 Sadovskaya, Victoria 6 Breden, Maxime 6 Castelli, Roberto 6 Chierchia, Luigi 6 Kalinin, Boris 6 Li, Xuemei 6 Wang, Yanan 6 Wiggins, Stephen 5 Arioli, Gianni 5 Bach, Volker 5 Backes, Lucas H. 5 Caffarelli, Luis Ángel 5 Cicalese, Marco 5 Cozzi, Matteo 5 Damjanović, Danijela 5 Gogolev, Andrey 5 Kim, Panki 5 Krauskopf, Bernd 5 Lu, Kening 5 Mezić, Igor 5 Novaga, Matteo 5 Obaya, Rafael 5 Osinga, Hinke Maria 5 Pollicott, Mark 5 Qiu, Hua 5 Sevryuk, Mikhail Borisovich 5 Si, Jianguo 5 Su, Xifeng 5 Tompaidis, Stathis 5 Turaev, Dmitry V. 5 Yao, Zhengan 5 Zhang, Weinian 5 Zhang, Wenmeng 5 Zhao, Kun 4 Apte, Amit 4 Asaoka, Masayuki 4 Baldomá, Inmaculada 4 Bessa, Mário 4 Canadell, Marta 4 Chen, Zhen-Qing 4 Cheng, Hongyu 4 Corsi, Livia 4 Dairbekov, Nurlan S. 4 Dipierro, Serena 4 Du, Yi 4 ElBialy, Mohamed Sami 4 Gameiro, Marcio F. 4 García-Azpeitia, Carlos 4 Guardia, Marcel 4 Huguet, Gemma 4 Jiang, Miaohua 4 Kocsard, Alejandro 4 Miraglio, Pietro 4 Mramor, Blaz 4 Panayotaros, Panayotis 4 Peralta-Salas, Daniel 4 Rink, Bob W. 4 Rom-Kedar, Vered 4 Si, Wen 4 Simó, Carles 4 Sire, Yannick 4 Song, Renming 4 von der Mosel, Heiko 4 Wayne, Clarence Eugene 4 Xu, Junxiang 4 Yan, Jun 3 Ambrose, David M. 3 Banyaga, Augustin ...and 752 more Authors
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#### Cited in 168 Serials

 59 Communications in Mathematical Physics 57 Journal of Differential Equations 45 Physica D 27 Ergodic Theory and Dynamical Systems 27 SIAM Journal on Applied Dynamical Systems 26 Chaos 24 Journal of Statistical Physics 19 Journal of Dynamics and Differential Equations 19 Journal of Nonlinear Science 19 Discrete and Continuous Dynamical Systems 19 Regular and Chaotic Dynamics 17 Communications in Nonlinear Science and Numerical Simulation 16 Archive for Rational Mechanics and Analysis 16 Journal of Mathematical Physics 16 Nonlinearity 15 Celestial Mechanics and Dynamical Astronomy 14 Transactions of the American Mathematical Society 12 Advances in Mathematics 12 Journal of Functional Analysis 11 Mathematische Zeitschrift 9 Proceedings of the American Mathematical Society 8 Israel Journal of Mathematics 8 Inventiones Mathematicae 8 Calculus of Variations and Partial Differential Equations 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 SIAM Journal on Mathematical Analysis 7 Bulletin of the American Mathematical Society. New Series 7 Indagationes Mathematicae. New Series 7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 7 Experimental Mathematics 7 Annals of Mathematics. Second Series 7 Qualitative Theory of Dynamical Systems 6 Chaos, Solitons and Fractals 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 The Journal of Geometric Analysis 6 Journal of Modern Dynamics 5 Duke Mathematical Journal 5 Mathematische Annalen 5 Nonlinear Dynamics 5 Annales Henri Poincaré 5 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Mathematical Analysis and Applications 4 Annales de l’Institut Fourier 4 Geometric and Functional Analysis. GAFA 4 Journal of Difference Equations and Applications 4 Electronic Research Announcements of the American Mathematical Society 4 Physical Review Letters 4 Dynamical Systems 4 Journal of Computational Dynamics 3 Applicable Analysis 3 Communications on Pure and Applied Mathematics 3 Journal of Computational Physics 3 Journal of Mathematical Biology 3 Acta Mathematica 3 Journal of Computational and Applied Mathematics 3 Topology and its Applications 3 Journal of Economic Dynamics & Control 3 Boletim da Sociedade Brasileira de Matemática. Nova Série 3 Journal of Knot Theory and its Ramifications 3 Journal of Mathematical Sciences (New York) 3 Communications in Contemporary Mathematics 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Journal of Applied Analysis and Computation 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Computers & Mathematics with Applications 2 Journal d’Analyse Mathématique 2 Physics Reports 2 Reviews of Modern Physics 2 Mathematics of Computation 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Commentarii Mathematici Helvetici 2 Geometriae Dedicata 2 Publications Mathématiques 2 Journal of Approximation Theory 2 Memoirs of the American Mathematical Society 2 Monatshefte für Mathematik 2 Systems & Control Letters 2 Applications of Mathematics 2 Communications in Partial Differential Equations 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Annales de l’Institut Henri Poincaré. Physique Théorique 2 Continuum Mechanics and Thermodynamics 2 Potential Analysis 2 Interfaces and Free Boundaries 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Foundations of Computational Mathematics 2 Advanced Nonlinear Studies 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Communications on Pure and Applied Analysis 2 Milan Journal of Mathematics 2 Advances in Difference Equations 2 Proceedings of the Steklov Institute of Mathematics 2 Journal of Fixed Point Theory and Applications 2 Frontiers of Mathematics in China 2 Discrete and Continuous Dynamical Systems. Series S 2 Analysis & PDE 2 Journal of Geometric Mechanics 2 Science China. Mathematics 2 Molecular Based Mathematical Biology ...and 68 more Serials
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#### Cited in 49 Fields

 538 Dynamical systems and ergodic theory (37-XX) 179 Partial differential equations (35-XX) 167 Mechanics of particles and systems (70-XX) 115 Ordinary differential equations (34-XX) 76 Numerical analysis (65-XX) 71 Differential geometry (53-XX) 69 Statistical mechanics, structure of matter (82-XX) 56 Fluid mechanics (76-XX) 44 Global analysis, analysis on manifolds (58-XX) 41 Calculus of variations and optimal control; optimization (49-XX) 37 Manifolds and cell complexes (57-XX) 36 Operator theory (47-XX) 30 Quantum theory (81-XX) 22 Probability theory and stochastic processes (60-XX) 21 Biology and other natural sciences (92-XX) 15 Mechanics of deformable solids (74-XX) 12 Functional analysis (46-XX) 11 Topological groups, Lie groups (22-XX) 11 General topology (54-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 9 Real functions (26-XX) 6 Functions of a complex variable (30-XX) 6 Difference and functional equations (39-XX) 6 Computer science (68-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Convex and discrete geometry (52-XX) 4 Algebraic topology (55-XX) 4 Geophysics (86-XX) 3 Number theory (11-XX) 3 Algebraic geometry (14-XX) 3 Measure and integration (28-XX) 3 Potential theory (31-XX) 3 Approximations and expansions (41-XX) 3 Integral equations (45-XX) 3 Optics, electromagnetic theory (78-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Special functions (33-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geometry (51-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Sequences, series, summability (40-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX)