# zbMATH — the first resource for mathematics

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 Documents Indexed: 48 Publications since 2000
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#### Co-Authors

 13 single-authored 8 Krikorian, Raphaël 4 Dolgopyat, Dmitry 3 Avila Cordeiro de Melo, Artur 3 Bounemoura, Abed 3 Eliasson, L. Hakan 3 Katok, Anatole B. 3 Niederman, Laurent 3 Saprykina, Maria 3 Windsor, Alistair 2 Bochi, Jairo 2 Kanigowski, Adam 2 Zhang, Zhiyuan 1 Damjanović, Danijela 1 Khanin, Konstantin M. 1 Kocsard, Alejandro 1 Le Calvez, Patrice 1 Lemańczyk, Mariusz 1 Pujals, Enrique Ramiro 1 Qu, Yanhui 1 Thouvenot, Jean-Paul 1 Vinogradov, Ilya 1 Xu, Disheng
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#### Serials

 6 Ergodic Theory and Dynamical Systems 3 Inventiones Mathematicae 3 Journal of Modern Dynamics 2 Nonlinearity 2 Acta Arithmetica 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Duke Mathematical Journal 2 Geometric and Functional Analysis. GAFA 2 Moscow Mathematical Journal 1 Communications in Mathematical Physics 1 Advances in Mathematics 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Commentarii Mathematici Helvetici 1 Publications Mathématiques 1 Journal of Differential Geometry 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Proceedings of the American Mathematical Society 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 Discrete and Continuous Dynamical Systems 1 Annals of Mathematics. Second Series 1 Regular and Chaotic Dynamics 1 Annales Henri Poincaré 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal de l’École Polytechnique – Mathématiques
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#### Fields

 47 Dynamical systems and ergodic theory (37-XX) 6 Number theory (11-XX) 5 Mechanics of particles and systems (70-XX) 4 Measure and integration (28-XX) 2 Ordinary differential equations (34-XX) 2 Probability theory and stochastic processes (60-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX)

#### Citations contained in zbMATH

41 Publications have been cited 349 times in 243 Documents Cited by Year
Constructions in elliptic dynamics. Zbl 1089.37012
2004
A KAM scheme for SL(2, $$\mathbb R$$) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
2011
Rigidity results for quasiperiodic $$\mathrm{SL}(2, \mathbb R)$$-cocycles. Zbl 1191.37007
2009
Herman’s last geometric theorem. Zbl 1175.37062
2009
Mixing in the absence of the shrinking target property. Zbl 1194.37013
2006
Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary. Zbl 1090.37001
2005
Analytic mixing reparametrizations of irrational flows. Zbl 1136.37307
2002
Weak mixing for reparameterized linear flows on the torus. Zbl 1001.37006
2002
Non-standard smooth realizations of Liouville rotations. Zbl 1127.37008
Fayad, B. R.; Saprykina, M.; Windsor, A.
2007
Around the stability of KAM tori. Zbl 1366.37126
Eliasson, L. H.; Fayad, B.; Krikorian, R.
2015
Multiple mixing for a class of conservative surface flows. Zbl 1358.37018
2016
Smooth linearization of commuting circle diffeomorphisms. Zbl 1177.37045
2009
Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for $$SL(2,\mathbb R )$$ cocycles. Zbl 1130.37027
2006
Polynomial decay of correlations for a class of smooth flows on the two torus. Zbl 1187.37009
2001
A remark on conservative diffeomorphisms. Zbl 1097.37010
Bochi, Jairo; Fayad, Bassam R.; Pujals, Enrique
2006
Unbounded orbits for semicircular outer billiard. Zbl 1377.37063
2009
Deviations of ergodic sums for toral translations. I. Convex bodies. Zbl 1308.37007
2014
Rank one and mixing differentiable flows. Zbl 1064.37006
2005
Superexponential stability of quasi-periodic motion in Hamiltonian systems. Zbl 1375.37150
Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent
2017
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021
2014
Mixed spectrum reparameterizations of linear flows on $$\mathbb T^2$$. Zbl 1123.37300
Fayad, Bassam; Katok, Anatole; Windsor, Alistar
2001
Topologically mixing and minimal but not ergodic, analytic transformation on $$\mathbf T^5$$. Zbl 0970.37007
2000
On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015
Avila, Artur; Fayad, Bassam; Kocsard, Alejandro
2015
KAM-tori near an analytic elliptic fixed point. Zbl 1417.37212
Eliasson, L. Hakan; Fayad, Bassam; Krikorian, Raphaël
2013
Smooth mixing flows with purely singular spectra. Zbl 1099.37018
2006
Nekhoroshev estimates for steep real-analytic elliptic equilibrium points. Zbl 1429.37031
Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent
2020
Central limit theorems for simultaneous Diophantine approximations. Zbl 1387.60046
2017
Exponential growth of product of matrices in $$\text{SL}(2,{\mathbb{R}})$$. Zbl 1142.37024
2008
A dichotomy between discrete and continuous spectrum for a class of special flows over rotations. Zbl 1109.37004
2007
On the ergodicity of cylindrical transformations given by the logarithm. Zbl 1130.37341
2006
Rigidity times for a weakly mixing dynamical system which are not rigidity times for any irrational rotation. Zbl 1356.37008
2015
On the convergence to $$0$$ of $$m_n \xi \mod 1$$. Zbl 1310.11079
2014
On the ergodicity of the Weyl sums cocycle. Zbl 1153.11044
2006
Nonuniform hyperbolicity and elliptic dynamics. Zbl 1147.37320
2004
Skew products over translations on $${\mathbb T}^d$$, $$d \geq 2$$. Zbl 1142.37301
2002
KAM tori are no more than sticky. Zbl 1447.37060
2020
Super-exponential stability for generic real-analytic elliptic equilibrium points. Zbl 1442.37071
Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent
2020
Isolated elliptic fixed points for smooth Hamiltonians. Zbl 1385.37076
2017
Discrete and continuous spectra on laminations over Aubry-Mather sets. Zbl 1148.37035
2008
Topologically mixing flows with pure point spectrum. Zbl 1066.37004
2003
Partially mixing and locally rank 1 smooth transformations and flows on the torus $$\mathbb{T}^d, d\geq 3$$. Zbl 1011.37001
2001
Nekhoroshev estimates for steep real-analytic elliptic equilibrium points. Zbl 1429.37031
Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent
2020
KAM tori are no more than sticky. Zbl 1447.37060
2020
Super-exponential stability for generic real-analytic elliptic equilibrium points. Zbl 1442.37071
Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent
2020
Superexponential stability of quasi-periodic motion in Hamiltonian systems. Zbl 1375.37150
Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent
2017
Central limit theorems for simultaneous Diophantine approximations. Zbl 1387.60046
2017
Isolated elliptic fixed points for smooth Hamiltonians. Zbl 1385.37076
2017
Multiple mixing for a class of conservative surface flows. Zbl 1358.37018
2016
Around the stability of KAM tori. Zbl 1366.37126
Eliasson, L. H.; Fayad, B.; Krikorian, R.
2015
On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015
Avila, Artur; Fayad, Bassam; Kocsard, Alejandro
2015
Rigidity times for a weakly mixing dynamical system which are not rigidity times for any irrational rotation. Zbl 1356.37008
2015
Deviations of ergodic sums for toral translations. I. Convex bodies. Zbl 1308.37007
2014
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021
2014
On the convergence to $$0$$ of $$m_n \xi \mod 1$$. Zbl 1310.11079
2014
KAM-tori near an analytic elliptic fixed point. Zbl 1417.37212
Eliasson, L. Hakan; Fayad, Bassam; Krikorian, Raphaël
2013
A KAM scheme for SL(2, $$\mathbb R$$) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
2011
Rigidity results for quasiperiodic $$\mathrm{SL}(2, \mathbb R)$$-cocycles. Zbl 1191.37007
2009
Herman’s last geometric theorem. Zbl 1175.37062
2009
Smooth linearization of commuting circle diffeomorphisms. Zbl 1177.37045
2009
Unbounded orbits for semicircular outer billiard. Zbl 1377.37063
2009
Exponential growth of product of matrices in $$\text{SL}(2,{\mathbb{R}})$$. Zbl 1142.37024
2008
Discrete and continuous spectra on laminations over Aubry-Mather sets. Zbl 1148.37035
2008
Non-standard smooth realizations of Liouville rotations. Zbl 1127.37008
Fayad, B. R.; Saprykina, M.; Windsor, A.
2007
A dichotomy between discrete and continuous spectrum for a class of special flows over rotations. Zbl 1109.37004
2007
Mixing in the absence of the shrinking target property. Zbl 1194.37013
2006
Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for $$SL(2,\mathbb R )$$ cocycles. Zbl 1130.37027
2006
A remark on conservative diffeomorphisms. Zbl 1097.37010
Bochi, Jairo; Fayad, Bassam R.; Pujals, Enrique
2006
Smooth mixing flows with purely singular spectra. Zbl 1099.37018
2006
On the ergodicity of cylindrical transformations given by the logarithm. Zbl 1130.37341
2006
On the ergodicity of the Weyl sums cocycle. Zbl 1153.11044
2006
Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary. Zbl 1090.37001
2005
Rank one and mixing differentiable flows. Zbl 1064.37006
2005
Constructions in elliptic dynamics. Zbl 1089.37012
2004
Nonuniform hyperbolicity and elliptic dynamics. Zbl 1147.37320
2004
Topologically mixing flows with pure point spectrum. Zbl 1066.37004
2003
Analytic mixing reparametrizations of irrational flows. Zbl 1136.37307
2002
Weak mixing for reparameterized linear flows on the torus. Zbl 1001.37006
2002
Skew products over translations on $${\mathbb T}^d$$, $$d \geq 2$$. Zbl 1142.37301
2002
Polynomial decay of correlations for a class of smooth flows on the two torus. Zbl 1187.37009
2001
Mixed spectrum reparameterizations of linear flows on $$\mathbb T^2$$. Zbl 1123.37300
Fayad, Bassam; Katok, Anatole; Windsor, Alistar
2001
Partially mixing and locally rank 1 smooth transformations and flows on the torus $$\mathbb{T}^d, d\geq 3$$. Zbl 1011.37001
2001
Topologically mixing and minimal but not ergodic, analytic transformation on $$\mathbf T^5$$. Zbl 0970.37007
2000
all top 5

#### Cited by 287 Authors

 16 Fayad, Bassam R. 12 Avila Cordeiro de Melo, Artur 11 You, Jiangong 10 Zhou, Qi 9 Kunde, Philipp 8 Kanigowski, Adam 7 Xu, Junxiang 6 Crovisier, Sylvain 6 Oertel-Jäger, Tobias Hendrik 6 Zhang, Dongfeng 5 Bessa, Mário 5 Bounemoura, Abed 5 Jitomirskaya, Svetlana Ya. 4 Béguin, François 4 Chaika, Jonathan 4 Dolgopyat, Dmitry 4 Frączek, Krzysztof Marek 4 Ginzburg, Viktor L’vovich 4 Gürel, Basak Zehra 4 Haro, Àlex 4 Hou, Xuanji 4 Koropecki, Andres 4 Krikorian, Raphaël 4 Lemańczyk, Mariusz 4 Ulcigrai, Corinna 4 Varandas, Paulo 4 Zhang, Zhiyuan 3 Bochi, Jairo 3 Cheng, Hongyu 3 Figueras, Jordi-Lluís 3 Hu, Huyi 3 Karaliolios, Nikolaos 3 Kim, Donghan 3 Le Calvez, Patrice 3 Le Roux, Frédéric 3 Luque, Alejandro 3 Marklof, Jens 3 Marx, Christoph A. 3 Ravotti, Davide 3 Saprykina, Maria 3 Wang, Baowei 3 Wang, Jing 3 Wilkinson, Amie 3 Xu, XinDong 3 Zhang, Pengfei 2 Bäcker, Arnd 2 Banerjee, Shilpak 2 Björklund, Michael 2 Bonatti, Christian 2 Boroński, Jan P. 2 Bramham, Barney 2 Chavaudret, Claire 2 Chen, Jianyu 2 Conze, Jean-Pierre 2 Damjanović, Danijela 2 Danilenko, Alexandre I. 2 Dávalos, Pablo 2 Forni, Giovanni 2 Fuchs, Michael 2 Galatolo, Stefano 2 Giannakis, Dimitrios 2 Gorodnik, Alexander 2 Huang, Wen 2 Johnson, Russell Allan 2 Katok, Anatole B. 2 Kocsard, Alejandro 2 Kułaga-Przymus, Joanna 2 Lopes Dias, João 2 Lu, Xuezhu 2 Massetti, Jessica Elisa 2 Meiss, James D. 2 Morris, Ian D. 2 Nerurkar, Mahesh G. 2 Niederman, Laurent 2 Oprocha, Piotr 2 Pesin, Yakov Borisovich 2 Procesi, Michela 2 Ramírez, Felipe A. 2 Rodriguez-Hertz, Federico 2 Shen, Luming 2 Si, Jianguo 2 Tiedra de Aldecoa, Rafael 2 Wang, Yiqian 2 Xavier, Juliana C. 2 Xue, Jinxin 2 Zhao, Xin 1 Adouani, Abdelhamid 1 Arbieto, Alexander 1 Arnold, Maxim 1 Athreya, Jayadev S. 1 Badea, Catalin 1 Bedrossian, Jacob 1 Benhenda, Mostapha 1 Biasco, Luca 1 Bomfim, Thiago 1 Boshernitzan, Michael D. 1 Boubel, Charles 1 Brugali, Davide 1 Bugeaud, Yann 1 Cai, Ao ...and 187 more Authors
all top 5

#### Cited in 80 Serials

 23 Ergodic Theory and Dynamical Systems 18 Communications in Mathematical Physics 11 Inventiones Mathematicae 8 Journal of Differential Equations 8 Proceedings of the American Mathematical Society 7 Advances in Mathematics 7 Discrete and Continuous Dynamical Systems 7 Regular and Chaotic Dynamics 6 Nonlinearity 6 Mathematische Zeitschrift 6 Geometric and Functional Analysis. GAFA 6 Journal of Dynamics and Differential Equations 5 Israel Journal of Mathematics 5 Journal of Mathematical Analysis and Applications 5 Duke Mathematical Journal 5 Journal of Functional Analysis 5 Mathematische Annalen 5 Annales Henri Poincaré 4 Journal d’Analyse Mathématique 4 Journal of Statistical Physics 4 Commentarii Mathematici Helvetici 4 Transactions of the American Mathematical Society 4 Journal of Modern Dynamics 3 Proceedings of the London Mathematical Society. Third Series 3 Journal of the American Mathematical Society 3 Journal of the Institute of Mathematics of Jussieu 2 Acta Mathematica 2 Annales de l’Institut Fourier 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Publications Mathématiques 2 Indagationes Mathematicae. New Series 2 Chaos 2 Acta Mathematica Sinica. English Series 2 Qualitative Theory of Dynamical Systems 2 Dynamical Systems 2 Proceedings of the Steklov Institute of Mathematics 2 Discrete and Continuous Dynamical Systems. Series S 2 Arnold Mathematical Journal 1 Archive for Rational Mechanics and Analysis 1 Acta Arithmetica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 Compositio Mathematica 1 Fundamenta Mathematicae 1 Journal of Number Theory 1 Journal für die Reine und Angewandte Mathematik 1 Mathematika 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Software. Practice & Experience 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 The Journal of Geometric Analysis 1 Linear Algebra and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Journal of Nonlinear Science 1 Topological Methods in Nonlinear Analysis 1 Applied and Computational Harmonic Analysis 1 Finite Fields and their Applications 1 Selecta Mathematica. New Series 1 Electronic Communications in Probability 1 Doklady Mathematics 1 Differential Equations and Dynamical Systems 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Advances in Geometry 1 Foundations of Computational Mathematics 1 Advanced Nonlinear Studies 1 Stochastics and Dynamics 1 Communications on Pure and Applied Analysis 1 SIAM Journal on Applied Dynamical Systems 1 Frontiers of Mathematics in China 1 Electronic Research Announcements in Mathematical Sciences 1 Analysis & PDE 1 Science China. Mathematics 1 Journal of Spectral Theory 1 Communications in Mathematics and Statistics 1 Journal de l’École Polytechnique – Mathématiques 1 Complex Manifolds
all top 5

#### Cited in 30 Fields

 212 Dynamical systems and ergodic theory (37-XX) 34 Ordinary differential equations (34-XX) 30 Mechanics of particles and systems (70-XX) 16 Number theory (11-XX) 16 Measure and integration (28-XX) 16 Operator theory (47-XX) 13 Differential geometry (53-XX) 12 Partial differential equations (35-XX) 10 Manifolds and cell complexes (57-XX) 9 Probability theory and stochastic processes (60-XX) 8 General topology (54-XX) 8 Quantum theory (81-XX) 7 Topological groups, Lie groups (22-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Abstract harmonic analysis (43-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Functional analysis (46-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX)