## Avila Cordeiro de Melo, Artur

Compute Distance To:
 Author ID: avila.artur Published as: Avila, Artur; Avila, A. Homepage: http://w3.impa.br/~avila/ External Links: MGP · Wikidata · GND · IdRef · theses.fr Awards: Clay Research Award (2006) · EMS Prize (2008) · Fields Medal (2014)
 Documents Indexed: 94 Publications since 2001, including 1 Book 1 Contribution as Editor · 1 Further Contribution Biographic References: 8 Publications Co-Authors: 54 Co-Authors with 83 Joint Publications 950 Co-Co-Authors
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### Co-Authors

 12 single-authored 10 Bochi, Jairo 10 Viana, Marcelo 8 Jitomirskaya, Svetlana Yakovlevna 7 Lyubich, Mikhail 7 Wilkinson, Amie 6 Damanik, David 6 Moreira, Carlos Gustavo Tamm de Araujo 5 Yoccoz, Jean-Christophe 4 Fayad, Bassam R. 3 Forni, Giovanni 3 Gouëzel, Sébastien 3 Hubert, Pascal 3 Kocsard, Alejandro 3 Krikorian, Raphaël 3 Matheus, Carlos 3 Santamaria, Jimmy 2 Buff, Xavier 2 Chéritat, Arnaud 2 Crovisier, Sylvain 2 de Melo, Welington 2 Delecroix, Vincent 2 Leguil, Martin 2 Shen, Weixiao 2 Skripchenko, Alexandra 2 Ulcigrai, Corinna 2 Zhou, Qi 1 Abdenur, Flavio 1 Bufetov, Aleksandr Igorevich 1 Candela, Pablo 1 Cheraghi, Davoud 1 de Simoi, Jacopo 1 Dolgopyat, Dmitry 1 Duryev, Eduard 1 Eskin, Alex 1 Kahn, Jeremy Adam 1 Kaloshin, Vadim Yu. 1 Khanin, Konstantin M. 1 Last, Yoram 1 Le Calvez, Patrice 1 Liu, Xiaochuan 1 Martens, Marco 1 Marx, Christoph A. 1 Möller, Martin 1 Rassias, Michael Th. 1 Ravotti, Davide 1 Resende, Maria João 1 Roblin, Thomas 1 Sadel, Christian 1 Sarig, Omri M. 1 Simon, Barry 1 Tsujii, Masato 1 Xu, Disheng 1 You, Jiangong 1 Zhang, Zhenghe 1 Zhang, Zhiyuan
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### Serials

 8 Annals of Mathematics. Second Series 7 Inventiones Mathematicae 6 Journal of the European Mathematical Society (JEMS) 4 Communications in Mathematical Physics 4 Acta Mathematica 4 Duke Mathematical Journal 4 Publications Mathématiques 4 Journal of the American Mathematical Society 3 Bulletin de la Société Mathématique de France 3 Geometric and Functional Analysis. GAFA 3 Journal of Modern Dynamics 2 Israel Journal of Mathematics 2 Nonlinearity 2 Advances in Mathematics 2 Commentarii Mathematici Helvetici 2 Journal of Differential Geometry 2 Mathematische Annalen 2 Ergodic Theory and Dynamical Systems 2 Portugaliae Mathematica. Nova Série 2 Bulletin of the Brazilian Mathematical Society. New Series 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Journal für die Reine und Angewandte Mathematik 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Mathematical Research Letters 1 Discrete and Continuous Dynamical Systems 1 European Mathematical Society Newsletter 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Oberwolfach Reports 1 Astérisque 1 Analysis & PDE 1 Pure and Applied Functional Analysis
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### Fields

 84 Dynamical systems and ergodic theory (37-XX) 17 Operator theory (47-XX) 10 Quantum theory (81-XX) 7 Measure and integration (28-XX) 7 Several complex variables and analytic spaces (32-XX) 5 Ordinary differential equations (34-XX) 4 Difference and functional equations (39-XX) 4 Statistical mechanics, structure of matter (82-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX)

### Citations contained in zbMATH Open

86 Publications have been cited 1,419 times in 868 Documents Cited by Year
The Ten Martini problem. Zbl 1166.47031
Avila, Artur; Jitomirskaya, Svetlana
2009
Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033
Avila, Artur; Krikorian, Raphaël
2006
Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003
Avila, Artur; Forni, Giovanni
2007
Almost localization and almost reducibility. Zbl 1185.47028
Avila, Artur; Jitomirskaya, Svetlana
2010
Exponential mixing for the Teichmüller flow. Zbl 1263.37051
Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe
2006
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001
Avila, Artur; Viana, Marcelo
2007
Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054
Avila, Artur; Viana, Marcelo
2010
A KAM scheme for SL(2, $$\mathbb R$$) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
2011
Global theory of one-frequency Schrödinger operators. Zbl 1360.37072
Avila, Artur
2015
Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018
Avila, Artur; Lyubich, Mikhail; de Melo, Welington
2003
Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum. Zbl 1225.26031
Avila, Artur; Last, Yoram; Simon, Barry
2010
An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104
Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim
2016
On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023
Avila, Artur
2009
On the regularization of conservative maps. Zbl 1211.37029
Avila, Artur
2010
Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058
Avila, Artur; Lyubich, Mikhail
2008
Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo
2013
Complex one-frequency cocycles. Zbl 1351.37136
Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian
2014
Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084
Avila, Artur; Viana, Marcelo; Wilkinson, Amie
2015
Sharp phase transitions for the almost Mathieu operator. Zbl 06803180
Avila, Artur; You, Jiangong; Zhou, Qi
2017
Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012
Avila, Artur; Damanik, David
2005
Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021
Avila, Artur; Damanik, David
2008
Density of positive Lyapunov exponents for $$\text{SL}(2,\mathbb R)$$-cocycles. Zbl 1236.37031
Avila, Artur
2011
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012
Avila, Artur; Bochi, Jairo; Damanik, David
2009
Monotonic cocycles. Zbl 1356.37070
Avila, Artur; Krikorian, Raphaël
2015
Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029
Avila, Artur; Moreira, Carlos Gustavo
2005
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022
Avila, Artur; Bochi, Jairo
2012
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
2009
Spectral theory of extended Harper’s model and a question by Erdős and Szekeres. Zbl 1380.37019
Avila, A.; Jitomirskaya, S.; Marx, C. A.
2017
Diffeomorphisms with positive metric entropy. Zbl 1362.37017
Avila, A.; Crovisier, S.; Wilkinson, A.
2016
Siegel disks with smooth boundaries. Zbl 1076.37030
Avila, Artur; Buff, Xavier; Chéritat, Arnaud
2004
Uniformly hyperbolic finite-valued $$\mathrm{SL}(2,\mathbb R)$$-cocycles. Zbl 1201.37032
Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe
2010
Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow. Zbl 1287.58016
Avila, Artur; Gouëzel, Sébastien
2013
A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019
Avila, Artur; Bochi, Jairo
2002
Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001
Avila, Artur; Viana, Marcelo
2007
Symplectic and isometric $$\mathrm{SL}(2,\mathbb{R})$$-invariant subbundles of the Hodge bundle. Zbl 1387.14093
Avila, Artur; Eskin, Alex; Möller, Martin
2017
On the Hausdorff dimension of the Rauzy gasket. (Sur la dimension de Hausdorff de la baderne de Rauzy.) Zbl 1356.37018
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
2016
Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007
Avila, Artur; Bochi, Jairo; Damanik, David
2012
The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047
Avila, Artur; Lyubich, Mikhail
2011
On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077
Avila, Artur
2015
Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
2016
Smoothness of solenoidal attractors. Zbl 1106.37015
Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato
2006
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
2014
The visits to zero of a random walk driven by an irrational rotation. Zbl 1326.60060
Avila, A.; Dolgopyat, D.; Duryev, E.; Sarig, O.
2015
Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012
Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna
2011
A generic $$C^1$$ map has no absolutely continuous invariant probability measure. Zbl 1190.37018
Avila, Artur; Bochi, Jairo
2006
On rigidity of critical circle maps. Zbl 1314.37028
Avila, Artur
2013
Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052
Avila, Artur; Kocsard, Alejandro
2011
Nonuniform center bunching and the genericity of ergodicity among $$C^1$$ partially hyperbolic symplectomorphisms. Zbl 1191.37017
Avila, Artur; Bochi, Jairo; Wilkinson, Amie
2009
Cocycles over partially hyperbolic maps. Zbl 1350.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2013
$$C^1$$ density of stable ergodicity. Zbl 1458.37048
Avila, A.; Crovisier, S.; Wilkinson, A.
2021
Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033
Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan
2018
Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025
Avila, Artur; Jitomirskaya, Svetlana
2011
Statistical properties of unimodal maps. Zbl 1078.37030
Avila, Artur; Moreira, Carlos Gustavo
2005
Solving the Ten Martini problem. Zbl 1166.47303
Avila, Artur; Jitomirskaya, Svetlana
2006
Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005
Avila, Artur; Delecroix, Vincent
2016
Robust transitivity and topological mixing for $$C^1$$-flows. Zbl 1040.37013
Abdenur, Flavio; Avila, Artur; Bochi, Jairo
2004
Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021
Avila, Artur; Moreira, Carlos Gustavo
2003
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
2006
Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2018
Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033
Avila, Artur; Resende, Maria João
2012
$$\mathrm{SL}(2,\mathbb R)$$-invariant probability measures on the moduli spaces of translation surfaces are regular. Zbl 1316.37016
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2013
A uniform dichotomy for generic $$\mathrm{SL}(2,\mathbb R)$$ cocycles over a minimal base. Zbl 1217.37017
Avila, Artur; Bochi, Jairo
2007
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
2011
Infinitesimal perturbations of rational maps. Zbl 1073.37051
Avila, Artur
2002
Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004
Avila, Artur; Bufetov, Alexander
2007
Density of positive Lyapunov exponents for quasiperiodic SL$$(2, \mathbb R)$$-cocycles in arbitrary dimension. Zbl 1191.34051
Avila, Artur
2009
On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015
Avila, Artur; Fayad, Bassam; Kocsard, Alejandro
2015
Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012
Avila, Artur; Candela, Pablo
2016
Recurrence for the wind-tree model. Zbl 1436.37006
Avila, A.; Hubert, P.
2020
Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022
Avila, Artur; Moreira, Carlos Gustavo
2005
Convergence of an exact quantization scheme. Zbl 1068.81041
Avila, Artur
2004
Some monoids of Pisot matrices. Zbl 1445.15016
Avila, Artur; Delecroix, Vincent
2019
Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014
Avila, Artur; Viana, Marcelo
2005
Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059
Avila, Artur; Cheraghi, Davoud
2018
Weak mixing properties of interval exchange transformations & translation flows. (Propriétés de mélange faible des échanges d’intervalles et des flots de translation.) Zbl 1402.37002
Avila, Artur; Leguil, Martin
2018
Second phase transition line. Zbl 1416.37010
Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi
2018
The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2019
Bifurcations of unimodal maps. Zbl 1070.37018
Avila, Artur; Moreira, Carlos Gustavo
2003
Uniform exponential growth for some $$SL(2,\mathbb R)$$ matrix products. Zbl 1189.37060
Avila, Artur; Roblin, Thomas
2009
Cocycles over partially hyperbolic maps. Zbl 1417.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2013
Generic expanding maps without absolutely continuous invariant $$\sigma$$-finite measure. Zbl 1139.28005
Avila, Artur; Bochi, Jairo
2007
Dynamics of renormalization operators. Zbl 1252.37030
Avila, Artur
2011
On mixing diffeomorphisms of the disc. Zbl 1448.37052
Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
2020
Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028
Avila, Artur
2002
Non-differentiable irrational curves for $$C^1$$ twist map. Zbl 07457813
2022
Stable accessibility with $$2$$ dimensional center. Zbl 1472.37033
Avila, Artur; Viana, Marcelo
2020
Non-differentiable irrational curves for $$C^1$$ twist map. Zbl 07457813
2022
$$C^1$$ density of stable ergodicity. Zbl 1458.37048
Avila, A.; Crovisier, S.; Wilkinson, A.
2021
Recurrence for the wind-tree model. Zbl 1436.37006
Avila, A.; Hubert, P.
2020
On mixing diffeomorphisms of the disc. Zbl 1448.37052
Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
2020
Stable accessibility with $$2$$ dimensional center. Zbl 1472.37033
Avila, Artur; Viana, Marcelo
2020
Some monoids of Pisot matrices. Zbl 1445.15016
Avila, Artur; Delecroix, Vincent
2019
The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2019
Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033
Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan
2018
Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2018
Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059
Avila, Artur; Cheraghi, Davoud
2018
Weak mixing properties of interval exchange transformations & translation flows. (Propriétés de mélange faible des échanges d’intervalles et des flots de translation.) Zbl 1402.37002
Avila, Artur; Leguil, Martin
2018
Second phase transition line. Zbl 1416.37010
Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi
2018
Sharp phase transitions for the almost Mathieu operator. Zbl 06803180
Avila, Artur; You, Jiangong; Zhou, Qi
2017
Spectral theory of extended Harper’s model and a question by Erdős and Szekeres. Zbl 1380.37019
Avila, A.; Jitomirskaya, S.; Marx, C. A.
2017
Symplectic and isometric $$\mathrm{SL}(2,\mathbb{R})$$-invariant subbundles of the Hodge bundle. Zbl 1387.14093
Avila, Artur; Eskin, Alex; Möller, Martin
2017
An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104
Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim
2016
Diffeomorphisms with positive metric entropy. Zbl 1362.37017
Avila, A.; Crovisier, S.; Wilkinson, A.
2016
On the Hausdorff dimension of the Rauzy gasket. (Sur la dimension de Hausdorff de la baderne de Rauzy.) Zbl 1356.37018
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
2016
Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
2016
Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005
Avila, Artur; Delecroix, Vincent
2016
Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012
Avila, Artur; Candela, Pablo
2016
Global theory of one-frequency Schrödinger operators. Zbl 1360.37072
Avila, Artur
2015
Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084
Avila, Artur; Viana, Marcelo; Wilkinson, Amie
2015
Monotonic cocycles. Zbl 1356.37070
Avila, Artur; Krikorian, Raphaël
2015
On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077
Avila, Artur
2015
The visits to zero of a random walk driven by an irrational rotation. Zbl 1326.60060
Avila, A.; Dolgopyat, D.; Duryev, E.; Sarig, O.
2015
On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015
Avila, Artur; Fayad, Bassam; Kocsard, Alejandro
2015
Complex one-frequency cocycles. Zbl 1351.37136
Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian
2014
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
2014
Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo
2013
Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow. Zbl 1287.58016
Avila, Artur; Gouëzel, Sébastien
2013
On rigidity of critical circle maps. Zbl 1314.37028
Avila, Artur
2013
Cocycles over partially hyperbolic maps. Zbl 1350.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2013
$$\mathrm{SL}(2,\mathbb R)$$-invariant probability measures on the moduli spaces of translation surfaces are regular. Zbl 1316.37016
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
2013
Cocycles over partially hyperbolic maps. Zbl 1417.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2013
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022
Avila, Artur; Bochi, Jairo
2012
Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007
Avila, Artur; Bochi, Jairo; Damanik, David
2012
Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033
Avila, Artur; Resende, Maria João
2012
A KAM scheme for SL(2, $$\mathbb R$$) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
2011
Density of positive Lyapunov exponents for $$\text{SL}(2,\mathbb R)$$-cocycles. Zbl 1236.37031
Avila, Artur
2011
The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047
Avila, Artur; Lyubich, Mikhail
2011
Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012
Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna
2011
Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052
Avila, Artur; Kocsard, Alejandro
2011
Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025
Avila, Artur; Jitomirskaya, Svetlana
2011
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
2011
Dynamics of renormalization operators. Zbl 1252.37030
Avila, Artur
2011
Almost localization and almost reducibility. Zbl 1185.47028
Avila, Artur; Jitomirskaya, Svetlana
2010
Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054
Avila, Artur; Viana, Marcelo
2010
Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum. Zbl 1225.26031
Avila, Artur; Last, Yoram; Simon, Barry
2010
On the regularization of conservative maps. Zbl 1211.37029
Avila, Artur
2010
Uniformly hyperbolic finite-valued $$\mathrm{SL}(2,\mathbb R)$$-cocycles. Zbl 1201.37032
Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe
2010
The Ten Martini problem. Zbl 1166.47031
Avila, Artur; Jitomirskaya, Svetlana
2009
On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023
Avila, Artur
2009
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012
Avila, Artur; Bochi, Jairo; Damanik, David
2009
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
2009
Nonuniform center bunching and the genericity of ergodicity among $$C^1$$ partially hyperbolic symplectomorphisms. Zbl 1191.37017
Avila, Artur; Bochi, Jairo; Wilkinson, Amie
2009
Density of positive Lyapunov exponents for quasiperiodic SL$$(2, \mathbb R)$$-cocycles in arbitrary dimension. Zbl 1191.34051
Avila, Artur
2009
Uniform exponential growth for some $$SL(2,\mathbb R)$$ matrix products. Zbl 1189.37060
Avila, Artur; Roblin, Thomas
2009
Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058
Avila, Artur; Lyubich, Mikhail
2008
Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021
Avila, Artur; Damanik, David
2008
Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003
Avila, Artur; Forni, Giovanni
2007
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001
Avila, Artur; Viana, Marcelo
2007
Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001
Avila, Artur; Viana, Marcelo
2007
A uniform dichotomy for generic $$\mathrm{SL}(2,\mathbb R)$$ cocycles over a minimal base. Zbl 1217.37017
Avila, Artur; Bochi, Jairo
2007
Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004
Avila, Artur; Bufetov, Alexander
2007
Generic expanding maps without absolutely continuous invariant $$\sigma$$-finite measure. Zbl 1139.28005
Avila, Artur; Bochi, Jairo
2007
Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033
Avila, Artur; Krikorian, Raphaël
2006
Exponential mixing for the Teichmüller flow. Zbl 1263.37051
Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe
2006
Smoothness of solenoidal attractors. Zbl 1106.37015
Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato
2006
A generic $$C^1$$ map has no absolutely continuous invariant probability measure. Zbl 1190.37018
Avila, Artur; Bochi, Jairo
2006
Solving the Ten Martini problem. Zbl 1166.47303
Avila, Artur; Jitomirskaya, Svetlana
2006
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
2006
Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012
Avila, Artur; Damanik, David
2005
Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029
Avila, Artur; Moreira, Carlos Gustavo
2005
Statistical properties of unimodal maps. Zbl 1078.37030
Avila, Artur; Moreira, Carlos Gustavo
2005
Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022
Avila, Artur; Moreira, Carlos Gustavo
2005
Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014
Avila, Artur; Viana, Marcelo
2005
Siegel disks with smooth boundaries. Zbl 1076.37030
Avila, Artur; Buff, Xavier; Chéritat, Arnaud
2004
Robust transitivity and topological mixing for $$C^1$$-flows. Zbl 1040.37013
Abdenur, Flavio; Avila, Artur; Bochi, Jairo
2004
Convergence of an exact quantization scheme. Zbl 1068.81041
Avila, Artur
2004
Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018
Avila, Artur; Lyubich, Mikhail; de Melo, Welington
2003
Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021
Avila, Artur; Moreira, Carlos Gustavo
2003
Bifurcations of unimodal maps. Zbl 1070.37018
Avila, Artur; Moreira, Carlos Gustavo
2003
A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019
Avila, Artur; Bochi, Jairo
2002
Infinitesimal perturbations of rational maps. Zbl 1073.37051
Avila, Artur
2002
Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028
Avila, Artur
2002
all top 5

### Cited by 803 Authors

 46 Avila Cordeiro de Melo, Artur 31 Damanik, David 27 Jitomirskaya, Svetlana Yakovlevna 15 Bochi, Jairo 15 You, Jiangong 14 Viana, Marcelo 12 Fillman, Jake 12 Matheus, Carlos 12 Zhou, Qi 11 Liu, Wencai 10 Forni, Giovanni 10 Rodriguez-Hertz, Federico 10 Ulcigrai, Corinna 10 Varandas, Paulo 10 Yang, Jiagang 9 Bessa, Mário 9 Breuer, Jonathan 9 Gorodetskii, Anton Semenovich 9 Xu, Junxiang 9 Yoccoz, Jean-Christophe 9 Zhang, Dongfeng 8 Araújo, Vítor 8 Crovisier, Sylvain 8 Hubert, Pascal 8 Kanigowski, Adam 8 Lubinsky, Doron S. 8 Lyubich, Mikhail 8 Tahzibi, Ali 8 Wang, Jing 8 Wilkinson, Amie 8 Zhao, Xin 7 Baladi, Viviane 7 Bjerklöv, Kristian 7 Bufetov, Aleksandr Igorevich 7 Chaika, Jonathan 7 Eskin, Alex 7 Ferenczi, Sébastien 7 Han, Rui 7 Krüger, Helge 7 Rodriguez Hertz, Jana 7 Wright, Alex 7 Yuan, Xiaoping 6 Butterley, Oliver 6 Carrasco, Pablo D. 6 de Melo, Welington 6 Guarino, Pablo 6 Hou, Xuanji 6 Kaloshin, Vadim Yu. 6 Masur, Howard A. 6 Rempe-Gillen, Lasse 6 Sadovskaya, Victoria 6 Xu, Disheng 5 Backes, Lucas H. 5 Bruin, Henk 5 Damjanović, Danijela 5 Gan, Zheng 5 Gelfert, Katrin Grit 5 Goldstein, Michael 5 Gouëzel, Sébastien 5 Oertel-Jäger, Tobias Hendrik 5 Kocsard, Alejandro 5 Krikorian, Raphaël 5 Last, Yoram 5 Marx, Christoph A. 5 Melbourne, Ian 5 Mirzakhani, Maryam 5 Morris, Ian D. 5 Ong, Darren C. 5 Poletti, Mauricio 5 Pollicott, Mark 5 Rams, Michał 5 Shen, Weixiao 5 Skripchenko, Alexandra 5 Smania, Daniel 5 Tao, Kai 5 van Strien, Sebastian J. 5 Yang, Fan 5 Zhang, Zhiyuan 4 Berger, Pierre 4 Bialy, Misha 4 Boissy, Corentin 4 Buff, Xavier 4 Cao, Yongluo 4 Chéritat, Arnaud 4 Dolgopyat, Dmitry 4 Dudko, Artem 4 Fayad, Bassam R. 4 Ge, Lingrui 4 Iommi, Godofredo 4 Khanin, Konstantin M. 4 Klein, Silvius 4 Kocić, Saša 4 Lanneau, Erwan 4 Liang, Jinhao 4 Liverani, Carlangelo 4 Lukic, Milivoje 4 Marin, Karina 4 Qu, Yanhui 4 Ravotti, Davide 4 Rocha, Jorge ...and 703 more Authors
all top 5

### Cited in 166 Serials

 81 Ergodic Theory and Dynamical Systems 75 Communications in Mathematical Physics 30 Inventiones Mathematicae 29 Discrete and Continuous Dynamical Systems 26 Advances in Mathematics 26 Proceedings of the American Mathematical Society 25 Journal of Functional Analysis 22 Journal of Modern Dynamics 21 Journal of the European Mathematical Society (JEMS) 20 Transactions of the American Mathematical Society 19 Annals of Mathematics. Second Series 16 Nonlinearity 15 Duke Mathematical Journal 15 Geometric and Functional Analysis. GAFA 14 Israel Journal of Mathematics 14 Journal of Statistical Physics 14 Journal of Dynamics and Differential Equations 13 Journal of Mathematical Physics 12 Journal of Spectral Theory 11 Journal d’Analyse Mathématique 11 Journal of the American Mathematical Society 11 Annales Henri Poincaré 10 Journal of Differential Equations 10 Mathematische Zeitschrift 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Journal of Mathematical Analysis and Applications 8 Annales de l’Institut Fourier 8 Geometriae Dedicata 7 Mathematische Annalen 7 Chaos 6 Publications Mathématiques 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Journal de l’École Polytechnique – Mathématiques 5 Letters in Mathematical Physics 5 Mathematical Proceedings of the Cambridge Philosophical Society 5 Acta Mathematica 5 Constructive Approximation 5 Journal of Difference Equations and Applications 5 Dynamical Systems 4 Commentarii Mathematici Helvetici 4 Journal of Approximation Theory 4 Memoirs of the American Mathematical Society 4 Monatshefte für Mathematik 4 Mathematical Physics, Analysis and Geometry 4 Acta Mathematica Sinica. English Series 4 Discrete and Continuous Dynamical Systems. Series B 4 Journal of the Institute of Mathematics of Jussieu 4 Frontiers of Mathematics in China 3 Mathematical Notes 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Proceedings of the London Mathematical Society. Third Series 3 Acta Applicandae Mathematicae 3 Physica D 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Bulletin of the American Mathematical Society. New Series 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Experimental Mathematics 3 Geometry & Topology 3 Regular and Chaotic Dynamics 3 Qualitative Theory of Dynamical Systems 3 Portugaliae Mathematica. Nova Série 3 Communications on Pure and Applied Analysis 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Proceedings of the Steklov Institute of Mathematics 3 Science China. Mathematics 3 Arnold Mathematical Journal 2 Applicable Analysis 2 Indian Journal of Pure & Applied Mathematics 2 Russian Mathematical Surveys 2 Bulletin de la Société Mathématique de France 2 Mathematische Nachrichten 2 Probability Theory and Related Fields 2 L’Enseignement Mathématique. 2e Série 2 SIAM Review 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Doklady Mathematics 2 Conformal Geometry and Dynamics 2 Communications in Nonlinear Science and Numerical Simulation 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Stochastics and Dynamics 2 Bulletin of the Brazilian Mathematical Society. New Series 2 SIAM Journal on Applied Dynamical Systems 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Journal of Fixed Point Theory and Applications 2 Journal of Physics A: Mathematical and Theoretical 2 Discrete and Continuous Dynamical Systems. Series S 2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Journal of Siberian Federal University. Mathematics & Physics 1 Communications on Pure and Applied Mathematics 1 Linear and Multilinear Algebra 1 Mathematical Biosciences 1 Mathematics of Computation 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Automatica 1 Compositio Mathematica 1 Dissertationes Mathematicae 1 Functional Analysis and its Applications ...and 66 more Serials
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### Cited in 48 Fields

 655 Dynamical systems and ergodic theory (37-XX) 131 Operator theory (47-XX) 86 Quantum theory (81-XX) 73 Ordinary differential equations (34-XX) 62 Partial differential equations (35-XX) 57 Statistical mechanics, structure of matter (82-XX) 54 Functions of a complex variable (30-XX) 52 Measure and integration (28-XX) 48 Several complex variables and analytic spaces (32-XX) 42 Probability theory and stochastic processes (60-XX) 33 Difference and functional equations (39-XX) 30 Number theory (11-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 22 Mechanics of particles and systems (70-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 20 Manifolds and cell complexes (57-XX) 19 Algebraic geometry (14-XX) 19 Differential geometry (53-XX) 14 Global analysis, analysis on manifolds (58-XX) 13 Topological groups, Lie groups (22-XX) 12 Computer science (68-XX) 11 Convex and discrete geometry (52-XX) 10 Functional analysis (46-XX) 8 Combinatorics (05-XX) 8 Special functions (33-XX) 7 Real functions (26-XX) 7 Potential theory (31-XX) 7 General topology (54-XX) 6 Numerical analysis (65-XX) 6 Optics, electromagnetic theory (78-XX) 3 General and overarching topics; collections (00-XX) 3 Group theory and generalizations (20-XX) 3 Approximations and expansions (41-XX) 3 Fluid mechanics (76-XX) 3 Biology and other natural sciences (92-XX) 2 History and biography (01-XX) 2 Mathematical logic and foundations (03-XX) 2 Integral transforms, operational calculus (44-XX) 2 Algebraic topology (55-XX) 2 Statistics (62-XX) 2 Systems theory; control (93-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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