Edit Profile (opens in new tab) Avila, Artur Co-Author Distance Author ID: avila.artur Published as: Avila, Artur; Avila, A. Further Spellings: Avila Cordeiro de Melo, Artur Homepage: https://www.math.uzh.ch/index.php?id=people&key1=4090 External Links: MGP · Wikidata · GND · IdRef · theses.fr Awards: Clay Research Award (2006) · EMS Prize (2008) · Fields Medal (2014) Documents Indexed: 111 Publications since 2001, including 1 Book and 12 Additional arXiv Preprints 2 Contributions as Editor · 1 Further Contribution Biographic References: 9 Publications Co-Authors: 60 Co-Authors with 96 Joint Publications 1,536 Co-Co-Authors all top 5 Co-Authors 18 single-authored 11 Bochi, Jairo 11 Viana, Marcelo 9 Damanik, David 8 Jitomirskaya, Svetlana Yakovlevna 8 Wilkinson, Amie 7 Lyubich, Mikhail 7 Moreira, Carlos Gustavo Tamm de Araujo 5 Yoccoz, Jean-Christophe 4 Fayad, Bassam R. 4 Forni, Giovanni 4 Zhou, Qi 3 Crovisier, Sylvain 3 Gouëzel, Sébastien 3 Hubert, Pascal 3 Kocsard, Alejandro 3 Krikorian, Raphaël 3 Matheus, Carlos 3 Santamaria, Jimmy 3 Zhang, Zhenghe 2 Buff, Xavier 2 Cheraghi, Davoud 2 Chéritat, Arnaud 2 de Melo, Welington 2 Delecroix, Vincent 2 Eskin, Alex 2 Last, Yoram 2 Leguil, Martin 2 Rassias, Michael Th. 2 Shen, Weixiao 2 Skripchenko, Alexandra 2 Ulcigrai, Corinna 2 You, Jiangong 1 Abdenur, Flavio 1 Bufetov, Aleksandr Igorevich 1 Candela, Pablo 1 de Simoi, Jacopo 1 Dolgopyat, Dmitry 1 Duryev, Eduard 1 Eliad, Alexander 1 Gorodetskii, Anton Semenovich 1 Kahn, Jeremy Adam 1 Kaloshin, Vadim Yu. 1 Khanin, Konstantin M. 1 Le Calvez, Patrice 1 Liu, Xiaochuan 1 Martens, Marco 1 Marx, Christoph A. 1 Möller, Martin 1 Ravotti, Davide 1 Resende, Maria João 1 Roblin, Thomas 1 Sadel, Christian 1 Safaee, Pedram 1 Sarig, Omri M. 1 Shamis, Mira 1 Simon, Barry 1 Sinaĭ, Yakov Grigor’evich 1 Tsujii, Masato 1 Xu, Disheng 1 Zhang, Zhiyuan all top 5 Serials 8 Inventiones Mathematicae 8 Annals of Mathematics. Second Series 6 Journal of the European Mathematical Society (JEMS) 5 Geometric and Functional Analysis. GAFA 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 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 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 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 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 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 all top 5 Fields 90 Dynamical systems and ergodic theory (37-XX) 19 Operator theory (47-XX) 11 Quantum theory (81-XX) 7 Measure and integration (28-XX) 7 Several complex variables and analytic spaces (32-XX) 6 Ordinary differential equations (34-XX) 5 Difference and functional equations (39-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Functions of a complex variable (30-XX) 3 Number theory (11-XX) 3 Partial differential equations (35-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Probability theory and stochastic processes (60-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Differential geometry (53-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 94 Publications have been cited 2,031 times in 1,166 Documents Cited by ▼ Year ▼ The Ten Martini problem. Zbl 1166.47031 Avila, Artur; Jitomirskaya, Svetlana 141 2009 Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033 Avila, Artur; Krikorian, Raphaël 112 2006 Exponential mixing for the Teichmüller flow. Zbl 1263.37051 Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe 89 2006 Almost localization and almost reducibility. Zbl 1185.47028 Avila, Artur; Jitomirskaya, Svetlana 88 2010 A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies. Zbl 1277.37089 Avila, Artur; Fayad, Bassam; Krikorian, Raphaël 86 2011 Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003 Avila, Artur; Forni, Giovanni 82 2007 Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054 Avila, Artur; Viana, Marcelo 82 2010 Global theory of one-frequency Schrödinger operators. Zbl 1360.37072 Avila, Artur 81 2015 Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001 Avila, Artur; Viana, Marcelo 61 2007 Sharp phase transitions for the almost Mathieu operator. Zbl 1503.47041 Avila, Artur; You, Jiangong; Zhou, Qi 48 2017 Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018 Avila, Artur; Lyubich, Mikhail; de Melo, Welington 42 2003 An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104 Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim 39 2016 Spectral theory of extended Harper’s model and a question by Erdős and Szekeres. Zbl 1380.37019 Avila, A.; Jitomirskaya, S.; Marx, C. A. 36 2017 Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005 Avila, Artur; Santamaria, Jimmy; Viana, Marcelo 31 2013 Complex one-frequency cocycles. Zbl 1351.37136 Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian 31 2014 Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058 Avila, Artur; Lyubich, Mikhail 30 2008 On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023 Avila, Artur 30 2009 Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084 Avila, Artur; Viana, Marcelo; Wilkinson, Amie 30 2015 On the regularization of conservative maps. Zbl 1211.37029 Avila, Artur 30 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 29 2010 Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021 Avila, Artur; Damanik, David 28 2008 Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012 Avila, Artur; Bochi, Jairo; Damanik, David 28 2009 Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles. Zbl 1201.37032 Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe 28 2010 Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047 Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao 27 2009 Diffeomorphisms with positive metric entropy. Zbl 1362.37017 Avila, A.; Crovisier, S.; Wilkinson, A. 27 2016 Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012 Avila, Artur; Damanik, David 26 2005 Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029 Avila, Artur; Moreira, Carlos Gustavo 25 2005 Monotonic cocycles. Zbl 1356.37070 Avila, Artur; Krikorian, Raphaël 25 2015 Siegel disks with smooth boundaries. Zbl 1076.37030 Avila, Artur; Buff, Xavier; Chéritat, Arnaud 24 2004 Density of positive Lyapunov exponents for \(\text{SL}(2,\mathbb R)\)-cocycles. Zbl 1236.37031 Avila, Artur 23 2011 Symplectic and isometric \(\mathrm{SL}(2,\mathbb{R})\)-invariant subbundles of the Hodge bundle. Zbl 1387.14093 Avila, Artur; Eskin, Alex; Möller, Martin 23 2017 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 23 2013 Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022 Avila, Artur; Bochi, Jairo 22 2012 Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001 Avila, Artur; Viana, Marcelo 21 2007 \(C^1\) density of stable ergodicity. Zbl 1458.37048 Avila, A.; Crovisier, S.; Wilkinson, A. 21 2021 A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019 Avila, Artur; Bochi, Jairo 20 2002 Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007 Avila, Artur; Bochi, Jairo; Damanik, David 19 2012 The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047 Avila, Artur; Lyubich, Mikhail 18 2011 Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012 Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna 17 2011 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 17 2016 On rigidity of critical circle maps. Zbl 1314.37028 Avila, Artur 16 2013 Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030 Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra 15 2016 Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005 Avila, Artur; Delecroix, Vincent 15 2016 Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052 Avila, Artur; Kocsard, Alejandro 14 2011 Smoothness of solenoidal attractors. Zbl 1106.37015 Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato 14 2006 Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089 Avila, Artur; Damanik, David; Zhang, Zhenghe 14 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. 13 2015 On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077 Avila, Artur 13 2015 A generic \(C^1\) map has no absolutely continuous invariant probability measure. Zbl 1190.37018 Avila, Artur; Bochi, Jairo 12 2006 Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025 Avila, Artur; Jitomirskaya, Svetlana 11 2011 Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033 Avila, Artur; Resende, Maria João 11 2012 Recurrence for the wind-tree model. Zbl 1436.37006 Avila, A.; Hubert, P. 11 2020 Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076 Avila, Artur; Lyubich, Mikhail; Shen, Weixiao 11 2011 Nonuniform center bunching and the genericity of ergodicity among \(C^1\) partially hyperbolic symplectomorphisms. Zbl 1191.37017 Avila, Artur; Bochi, Jairo; Wilkinson, Amie 10 2009 Some monoids of Pisot matrices. Zbl 1445.15016 Avila, Artur; Delecroix, Vincent 10 2019 Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021 Avila, Artur; Moreira, Carlos Gustavo 9 2003 Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045 Avila, Artur; Lyubich, Mikhail 9 2006 Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033 Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan 9 2018 Cocycles over partially hyperbolic maps. Zbl 1350.37004 Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie 8 2013 Second phase transition line. Zbl 1416.37010 Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi 7 2018 Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088 Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 7 2018 Statistical properties of unimodal maps. Zbl 1078.37030 Avila, Artur; Moreira, Carlos Gustavo 7 2005 Solving the Ten Martini problem. Zbl 1166.47303 Avila, Artur; Jitomirskaya, Svetlana 7 2006 Robust transitivity and topological mixing for \(C^1\)-flows. Zbl 1040.37013 Abdenur, Flavio; Avila, Artur; Bochi, Jairo 7 2004 A uniform dichotomy for generic \(\mathrm{SL}(2,\mathbb R)\) cocycles over a minimal base. Zbl 1217.37017 Avila, Artur; Bochi, Jairo 7 2007 Mixing for smooth time-changes of general nilflows. Zbl 1479.37022 Avila, Artur; Forni, Giovanni; Ravotti, Davide; Ulcigrai, Corinna 7 2021 Lebesgue measure of Feigenbaum Julia sets. Zbl 1494.37026 Avila, Artur; Lyubich, Mikhail 7 2022 \(\mathrm{SL}(2,\mathbb R)\)-invariant probability measures on the moduli spaces of translation surfaces are regular. Zbl 1316.37016 Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 7 2013 Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004 Avila, Artur; Bufetov, Alexander 6 2007 Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022 Avila, Artur; Moreira, Carlos Gustavo 5 2005 Convergence of an exact quantization scheme. Zbl 1068.81041 Avila, Artur 5 2004 Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012 Avila, Artur; Candela, Pablo 5 2016 Infinitesimal perturbations of rational maps. Zbl 1073.37051 Avila, Artur 5 2002 Absolute continuity, Lyapunov exponents, and rigidity. II: Systems with compact center leaves. Zbl 1493.37022 Avila, A.; Viana, Marcelo; Wilkinson, A. 5 2022 Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059 Avila, Artur; Cheraghi, Davoud 5 2018 Density of positive Lyapunov exponents for quasiperiodic SL\((2, \mathbb R)\)-cocycles in arbitrary dimension. Zbl 1191.34051 Avila, Artur 4 2009 On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015 Avila, Artur; Fayad, Bassam; Kocsard, Alejandro 4 2015 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 4 2018 The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030 Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 4 2019 Dynamics of renormalization operators. Zbl 1252.37030 Avila, Artur 3 2011 Uniform exponential growth for some \(SL(2,\mathbb R)\) matrix products. Zbl 1189.37060 Avila, Artur; Roblin, Thomas 3 2009 Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014 Avila, Artur; Viana, Marcelo 3 2005 Schrödinger operators with potentials generated by hyperbolic transformations. I: Positivity of the Lyapunov exponent. Zbl 1511.37038 Avila, Artur; Damanik, David; Zhang, Zhenghe 3 2023 On mixing diffeomorphisms of the disc. Zbl 1448.37052 Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan 3 2020 Generic expanding maps without absolutely continuous invariant \(\sigma\)-finite measure. Zbl 1139.28005 Avila, Artur; Bochi, Jairo 2 2007 Bifurcations of unimodal maps. Zbl 1070.37018 Avila, Artur; Moreira, Carlos Gustavo 2 2003 The spectrum of Schrödinger operators with randomly perturbed ergodic potentials. Zbl 07680038 Avila, Artur; Damanik, David; Gorodetski, Anton 2 2023 Cocycles over partially hyperbolic maps. Zbl 1417.37004 Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie 2 2013 Stable accessibility with \(2\) dimensional center. Zbl 1472.37033 Avila, Artur; Viana, Marcelo 2 2020 Invariant graphs and spectral type of Schrödinger operators. Zbl 1472.35106 Avila, Artur; Khanin, Konstantin; Leguil, Martin 2 2020 Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028 Avila, Artur 1 2002 Non-differentiable irrational curves for \(C^1\) twist map. Zbl 1490.37057 Avila, Artur; Fayad, Bassam 1 2022 Quantitative weak mixing for interval exchange transformations. Zbl 1514.37012 Avila, Artur; Forni, Giovanni; Safaee, Pedram 1 2023 Analytic maps of parabolic and elliptic type with trivial centralisers. Zbl 1512.37051 Avila, Artur; Cheraghi, Davoud; Eliad, Alexander 1 2022 Schrödinger operators with potentials generated by hyperbolic transformations. I: Positivity of the Lyapunov exponent. Zbl 1511.37038 Avila, Artur; Damanik, David; Zhang, Zhenghe 3 2023 The spectrum of Schrödinger operators with randomly perturbed ergodic potentials. Zbl 07680038 Avila, Artur; Damanik, David; Gorodetski, Anton 2 2023 Quantitative weak mixing for interval exchange transformations. Zbl 1514.37012 Avila, Artur; Forni, Giovanni; Safaee, Pedram 1 2023 Lebesgue measure of Feigenbaum Julia sets. Zbl 1494.37026 Avila, Artur; Lyubich, Mikhail 7 2022 Absolute continuity, Lyapunov exponents, and rigidity. II: Systems with compact center leaves. Zbl 1493.37022 Avila, A.; Viana, Marcelo; Wilkinson, A. 5 2022 Non-differentiable irrational curves for \(C^1\) twist map. Zbl 1490.37057 Avila, Artur; Fayad, Bassam 1 2022 Analytic maps of parabolic and elliptic type with trivial centralisers. Zbl 1512.37051 Avila, Artur; Cheraghi, Davoud; Eliad, Alexander 1 2022 \(C^1\) density of stable ergodicity. Zbl 1458.37048 Avila, A.; Crovisier, S.; Wilkinson, A. 21 2021 Mixing for smooth time-changes of general nilflows. Zbl 1479.37022 Avila, Artur; Forni, Giovanni; Ravotti, Davide; Ulcigrai, Corinna 7 2021 Recurrence for the wind-tree model. Zbl 1436.37006 Avila, A.; Hubert, P. 11 2020 On mixing diffeomorphisms of the disc. Zbl 1448.37052 Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan 3 2020 Stable accessibility with \(2\) dimensional center. Zbl 1472.37033 Avila, Artur; Viana, Marcelo 2 2020 Invariant graphs and spectral type of Schrödinger operators. Zbl 1472.35106 Avila, Artur; Khanin, Konstantin; Leguil, Martin 2 2020 Some monoids of Pisot matrices. Zbl 1445.15016 Avila, Artur; Delecroix, Vincent 10 2019 The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030 Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 4 2019 Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033 Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan 9 2018 Second phase transition line. Zbl 1416.37010 Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi 7 2018 Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088 Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 7 2018 Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059 Avila, Artur; Cheraghi, Davoud 5 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 4 2018 Sharp phase transitions for the almost Mathieu operator. Zbl 1503.47041 Avila, Artur; You, Jiangong; Zhou, Qi 48 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. 36 2017 Symplectic and isometric \(\mathrm{SL}(2,\mathbb{R})\)-invariant subbundles of the Hodge bundle. Zbl 1387.14093 Avila, Artur; Eskin, Alex; Möller, Martin 23 2017 An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104 Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim 39 2016 Diffeomorphisms with positive metric entropy. Zbl 1362.37017 Avila, A.; Crovisier, S.; Wilkinson, A. 27 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 17 2016 Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030 Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra 15 2016 Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005 Avila, Artur; Delecroix, Vincent 15 2016 Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012 Avila, Artur; Candela, Pablo 5 2016 Global theory of one-frequency Schrödinger operators. Zbl 1360.37072 Avila, Artur 81 2015 Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084 Avila, Artur; Viana, Marcelo; Wilkinson, Amie 30 2015 Monotonic cocycles. Zbl 1356.37070 Avila, Artur; Krikorian, Raphaël 25 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. 13 2015 On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077 Avila, Artur 13 2015 On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015 Avila, Artur; Fayad, Bassam; Kocsard, Alejandro 4 2015 Complex one-frequency cocycles. Zbl 1351.37136 Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian 31 2014 Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089 Avila, Artur; Damanik, David; Zhang, Zhenghe 14 2014 Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005 Avila, Artur; Santamaria, Jimmy; Viana, Marcelo 31 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 23 2013 On rigidity of critical circle maps. Zbl 1314.37028 Avila, Artur 16 2013 Cocycles over partially hyperbolic maps. Zbl 1350.37004 Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie 8 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 7 2013 Cocycles over partially hyperbolic maps. Zbl 1417.37004 Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie 2 2013 Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022 Avila, Artur; Bochi, Jairo 22 2012 Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007 Avila, Artur; Bochi, Jairo; Damanik, David 19 2012 Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033 Avila, Artur; Resende, Maria João 11 2012 A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies. Zbl 1277.37089 Avila, Artur; Fayad, Bassam; Krikorian, Raphaël 86 2011 Density of positive Lyapunov exponents for \(\text{SL}(2,\mathbb R)\)-cocycles. Zbl 1236.37031 Avila, Artur 23 2011 The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047 Avila, Artur; Lyubich, Mikhail 18 2011 Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012 Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna 17 2011 Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052 Avila, Artur; Kocsard, Alejandro 14 2011 Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025 Avila, Artur; Jitomirskaya, Svetlana 11 2011 Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076 Avila, Artur; Lyubich, Mikhail; Shen, Weixiao 11 2011 Dynamics of renormalization operators. Zbl 1252.37030 Avila, Artur 3 2011 Almost localization and almost reducibility. Zbl 1185.47028 Avila, Artur; Jitomirskaya, Svetlana 88 2010 Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054 Avila, Artur; Viana, Marcelo 82 2010 On the regularization of conservative maps. Zbl 1211.37029 Avila, Artur 30 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 29 2010 Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles. Zbl 1201.37032 Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe 28 2010 The Ten Martini problem. Zbl 1166.47031 Avila, Artur; Jitomirskaya, Svetlana 141 2009 On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023 Avila, Artur 30 2009 Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012 Avila, Artur; Bochi, Jairo; Damanik, David 28 2009 Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047 Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao 27 2009 Nonuniform center bunching and the genericity of ergodicity among \(C^1\) partially hyperbolic symplectomorphisms. Zbl 1191.37017 Avila, Artur; Bochi, Jairo; Wilkinson, Amie 10 2009 Density of positive Lyapunov exponents for quasiperiodic SL\((2, \mathbb R)\)-cocycles in arbitrary dimension. Zbl 1191.34051 Avila, Artur 4 2009 Uniform exponential growth for some \(SL(2,\mathbb R)\) matrix products. Zbl 1189.37060 Avila, Artur; Roblin, Thomas 3 2009 Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058 Avila, Artur; Lyubich, Mikhail 30 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 28 2008 Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003 Avila, Artur; Forni, Giovanni 82 2007 Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001 Avila, Artur; Viana, Marcelo 61 2007 Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001 Avila, Artur; Viana, Marcelo 21 2007 A uniform dichotomy for generic \(\mathrm{SL}(2,\mathbb R)\) cocycles over a minimal base. Zbl 1217.37017 Avila, Artur; Bochi, Jairo 7 2007 Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004 Avila, Artur; Bufetov, Alexander 6 2007 Generic expanding maps without absolutely continuous invariant \(\sigma\)-finite measure. Zbl 1139.28005 Avila, Artur; Bochi, Jairo 2 2007 Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033 Avila, Artur; Krikorian, Raphaël 112 2006 Exponential mixing for the Teichmüller flow. Zbl 1263.37051 Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe 89 2006 Smoothness of solenoidal attractors. Zbl 1106.37015 Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato 14 2006 A generic \(C^1\) map has no absolutely continuous invariant probability measure. Zbl 1190.37018 Avila, Artur; Bochi, Jairo 12 2006 Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045 Avila, Artur; Lyubich, Mikhail 9 2006 Solving the Ten Martini problem. Zbl 1166.47303 Avila, Artur; Jitomirskaya, Svetlana 7 2006 Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012 Avila, Artur; Damanik, David 26 2005 Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029 Avila, Artur; Moreira, Carlos Gustavo 25 2005 Statistical properties of unimodal maps. Zbl 1078.37030 Avila, Artur; Moreira, Carlos Gustavo 7 2005 Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022 Avila, Artur; Moreira, Carlos Gustavo 5 2005 Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014 Avila, Artur; Viana, Marcelo 3 2005 Siegel disks with smooth boundaries. Zbl 1076.37030 Avila, Artur; Buff, Xavier; Chéritat, Arnaud 24 2004 Robust transitivity and topological mixing for \(C^1\)-flows. Zbl 1040.37013 Abdenur, Flavio; Avila, Artur; Bochi, Jairo 7 2004 Convergence of an exact quantization scheme. Zbl 1068.81041 Avila, Artur 5 2004 Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018 Avila, Artur; Lyubich, Mikhail; de Melo, Welington 42 2003 Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021 Avila, Artur; Moreira, Carlos Gustavo 9 2003 Bifurcations of unimodal maps. Zbl 1070.37018 Avila, Artur; Moreira, Carlos Gustavo 2 2003 A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019 Avila, Artur; Bochi, Jairo 20 2002 Infinitesimal perturbations of rational maps. Zbl 1073.37051 Avila, Artur 5 2002 Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028 Avila, Artur 1 2002 all cited Publications top 5 cited Publications all top 5 Cited by 1,020 Authors 51 Avila, Artur 42 Damanik, David 29 Jitomirskaya, Svetlana Yakovlevna 22 You, Jiangong 19 Zhou, Qi 18 Fillman, Jake 16 Matheus, Carlos 16 Viana, Marcelo 15 Bochi, Jairo 13 Liu, Wencai 13 Yang, Jiagang 13 Zhang, Dongfeng 12 Forni, Giovanni 12 Rodriguez-Hertz, Federico 12 Ulcigrai, Corinna 11 Crovisier, Sylvain 11 Ge, Lingrui 11 Gorodetskii, Anton Semenovich 11 Xu, Junxiang 10 Araújo, Vítor 10 Gelfert, Katrin Grit 10 Guarino, Pablo 10 Hubert, Pascal 10 Kanigowski, Adam 10 Lubinsky, Doron S. 10 Tahzibi, Ali 10 Varandas, Paulo 10 Zhao, Xin 9 Bessa, Mário 9 Breuer, Jonathan 9 Cao, Yongluo 9 Lyubich, Mikhail 9 Sadovskaya, Victoria 9 Wang, Jing 9 Wilkinson, Amie 9 Wright, Alex 9 Yoccoz, Jean-Christophe 8 Bjerklöv, Kristian 8 Bufetov, Aleksandr Igorevich 8 Chaika, Jonathan 8 Eskin, Alex 8 Han, Rui 8 Hou, Xuanji 8 Kaloshin, Vadim Yu. 8 Pollicott, Mark 8 Zhang, Zhiyuan 7 Baladi, Viviane 7 de Faria, Edson 7 de Melo, Welington 7 Díaz, Lorenzo Justiniano 7 Duarte, Pedro 7 Ferenczi, Sébastien 7 Klein, Silvius 7 Krüger, Helge 7 Liang, Jinhao 7 Melbourne, Ian 7 Ong, Darren C. 7 Poletti, Mauricio 7 Rams, Michał 7 Rodriguez Hertz, Jana 7 Shi, Yunfeng 7 Smania, Daniel 7 Tao, Kai 7 van Strien, Sebastian J. 7 Yuan, Xiaoping 6 Apisa, Paul 6 Barrientos, Pablo G. 6 Bruin, Henk 6 Butterley, Oliver 6 Cai, Ao 6 Carrasco, Pablo D. 6 Cheng, Hongyu 6 Damjanović, Danijela 6 Kalinin, Boris 6 Khanin, Konstantin M. 6 Krikorian, Raphaël 6 Liverani, Carlangelo 6 Masur, Howard A. 6 Mirzakhani, Maryam 6 Morris, Ian D. 6 Obata, Davi 6 Potrie, Rafael 6 Ravotti, Davide 6 Rempe-Gillen, Lasse 6 Skripchenko, Alexandra 6 Ures, Raúl 6 Xu, Disheng 6 Zhang, Zhenghe 5 Backes, Lucas H. 5 Berthé, Valérie 5 Bezerra, Jamerson 5 Bialy, Misha 5 Boissy, Corentin 5 Cheraghi, Davoud 5 Chéritat, Arnaud 5 Clark, Trevor 5 de Simoi, Jacopo 5 Dudko, Artem 5 Fayad, Bassam R. 5 Fedotov, Alexander ...and 920 more Authors all top 5 Cited in 201 Serials 103 Ergodic Theory and Dynamical Systems 90 Communications in Mathematical Physics 40 Discrete and Continuous Dynamical Systems 38 Advances in Mathematics 36 Inventiones Mathematicae 34 Nonlinearity 31 Journal of Modern Dynamics 29 Journal of Functional Analysis 29 Proceedings of the American Mathematical Society 25 Journal of the European Mathematical Society (JEMS) 24 Annals of Mathematics. Second Series 23 Journal of Mathematical Physics 23 Transactions of the American Mathematical Society 22 Geometric and Functional Analysis. GAFA 21 Journal of Dynamics and Differential Equations 17 Journal of Statistical Physics 16 Israel Journal of Mathematics 16 Duke Mathematical Journal 16 Mathematische Zeitschrift 15 Journal of Spectral Theory 14 Journal of Differential Equations 14 Annales Henri Poincaré 12 Journal d’Analyse Mathématique 12 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 11 Journal of the American Mathematical Society 10 Geometriae Dedicata 10 Mathematische Annalen 9 Dynamical Systems 8 Journal of Mathematical Analysis and Applications 8 Annales de l’Institut Fourier 8 Publications Mathématiques 7 Bulletin de la Société Mathématique de France 7 Memoirs of the American Mathematical Society 7 Chaos 7 Journal de l’École Polytechnique – Mathématiques 6 Proceedings of the London Mathematical Society. Third Series 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Experimental Mathematics 6 Geometry & Topology 6 Qualitative Theory of Dynamical Systems 6 Communications on Pure and Applied Analysis 6 Journal of Physics A: Mathematical and Theoretical 6 Arnold Mathematical Journal 5 Letters in Mathematical Physics 5 Mathematical Proceedings of the Cambridge Philosophical Society 5 Acta Mathematica 5 Bulletin of the London Mathematical Society 5 Commentarii Mathematici Helvetici 5 Journal of the London Mathematical Society. Second Series 5 Constructive Approximation 5 Journal of Difference Equations and Applications 5 Regular and Chaotic Dynamics 5 Acta Mathematica Sinica. English Series 5 Discrete and Continuous Dynamical Systems. Series B 5 Journal of the Institute of Mathematics of Jussieu 5 Frontiers of Mathematics in China 4 Mathematical Notes 4 Journal of Approximation Theory 4 Monatshefte für Mathematik 4 Acta Mathematica Hungarica 4 Bulletin of the American Mathematical Society. New Series 4 Mathematical Physics, Analysis and Geometry 4 Stochastics and Dynamics 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 4 Oberwolfach Reports 3 Communications on Pure and Applied Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Nachrichten 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Transactions of the Moscow Mathematical Society 3 Acta Applicandae Mathematicae 3 Physica D 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Conformal Geometry and Dynamics 3 Communications in Nonlinear Science and Numerical Simulation 3 Portugaliae Mathematica. Nova Série 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 SIAM Journal on Applied Dynamical Systems 3 Proceedings of the Steklov Institute of Mathematics 3 Analysis & PDE 3 Science China. Mathematics 3 Journal of Siberian Federal University. Mathematics & Physics 2 Applicable Analysis 2 Indian Journal of Pure & Applied Mathematics 2 Russian Mathematical Surveys 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Compositio Mathematica 2 Pacific Journal of Mathematics 2 Topology and its Applications 2 Probability Theory and Related Fields 2 The Journal of Geometric Analysis 2 Annals of Physics 2 L’Enseignement Mathématique. 2e Série 2 Linear Algebra and its Applications 2 SIAM Review 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Journal of Nonlinear Science ...and 101 more Serials all top 5 Cited in 52 Fields 885 Dynamical systems and ergodic theory (37-XX) 180 Operator theory (47-XX) 127 Quantum theory (81-XX) 95 Ordinary differential equations (34-XX) 84 Partial differential equations (35-XX) 79 Functions of a complex variable (30-XX) 70 Several complex variables and analytic spaces (32-XX) 70 Statistical mechanics, structure of matter (82-XX) 68 Measure and integration (28-XX) 49 Probability theory and stochastic processes (60-XX) 48 Number theory (11-XX) 43 Difference and functional equations (39-XX) 41 Mechanics of particles and systems (70-XX) 29 Harmonic analysis on Euclidean spaces (42-XX) 27 Algebraic geometry (14-XX) 27 Manifolds and cell complexes (57-XX) 24 Differential geometry (53-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 22 Topological groups, Lie groups (22-XX) 19 Global analysis, analysis on manifolds (58-XX) 16 Convex and discrete geometry (52-XX) 15 Functional analysis (46-XX) 13 Computer science (68-XX) 11 Real functions (26-XX) 10 Combinatorics (05-XX) 10 General topology (54-XX) 9 Potential theory (31-XX) 8 Group theory and generalizations (20-XX) 8 Special functions (33-XX) 7 Optics, electromagnetic theory (78-XX) 6 General and overarching topics; collections (00-XX) 6 Numerical analysis (65-XX) 5 Approximations and expansions (41-XX) 4 History and biography (01-XX) 4 Mathematical logic and foundations (03-XX) 4 Fluid mechanics (76-XX) 4 Biology and other natural sciences (92-XX) 3 Integral transforms, operational calculus (44-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Algebraic topology (55-XX) 2 Abstract harmonic analysis (43-XX) 2 Geometry (51-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-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 Mechanics of deformable solids (74-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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