Edit Profile (opens in new tab) Avila Cordeiro de Melo, Artur Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 86 Publications have been cited 1,419 times in 868 Documents Cited by ▼ Year ▼ The Ten Martini problem. Zbl 1166.47031Avila, Artur; Jitomirskaya, Svetlana 102 2009 Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033Avila, Artur; Krikorian, Raphaël 80 2006 Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003Avila, Artur; Forni, Giovanni 63 2007 Almost localization and almost reducibility. Zbl 1185.47028Avila, Artur; Jitomirskaya, Svetlana 62 2010 Exponential mixing for the Teichmüller flow. Zbl 1263.37051Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe 62 2006 Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001Avila, Artur; Viana, Marcelo 55 2007 Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054Avila, Artur; Viana, Marcelo 54 2010 A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies. Zbl 1277.37089Avila, Artur; Fayad, Bassam; Krikorian, Raphaël 50 2011 Global theory of one-frequency Schrödinger operators. Zbl 1360.37072Avila, Artur 48 2015 Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018Avila, Artur; Lyubich, Mikhail; de Melo, Welington 35 2003 Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum. Zbl 1225.26031Avila, Artur; Last, Yoram; Simon, Barry 26 2010 An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim 25 2016 On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023Avila, Artur 25 2009 On the regularization of conservative maps. Zbl 1211.37029Avila, Artur 24 2010 Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058Avila, Artur; Lyubich, Mikhail 24 2008 Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005Avila, Artur; Santamaria, Jimmy; Viana, Marcelo 23 2013 Complex one-frequency cocycles. Zbl 1351.37136Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian 22 2014 Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084Avila, Artur; Viana, Marcelo; Wilkinson, Amie 22 2015 Sharp phase transitions for the almost Mathieu operator. Zbl 06803180Avila, Artur; You, Jiangong; Zhou, Qi 21 2017 Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012Avila, Artur; Damanik, David 21 2005 Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021Avila, Artur; Damanik, David 21 2008 Density of positive Lyapunov exponents for \(\text{SL}(2,\mathbb R)\)-cocycles. Zbl 1236.37031Avila, Artur 21 2011 Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012Avila, Artur; Bochi, Jairo; Damanik, David 20 2009 Monotonic cocycles. Zbl 1356.37070Avila, Artur; Krikorian, Raphaël 19 2015 Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029Avila, Artur; Moreira, Carlos Gustavo 19 2005 Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022Avila, Artur; Bochi, Jairo 19 2012 Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao 19 2009 Spectral theory of extended Harper’s model and a question by Erdős and Szekeres. Zbl 1380.37019Avila, A.; Jitomirskaya, S.; Marx, C. A. 19 2017 Diffeomorphisms with positive metric entropy. Zbl 1362.37017Avila, A.; Crovisier, S.; Wilkinson, A. 19 2016 Siegel disks with smooth boundaries. Zbl 1076.37030Avila, Artur; Buff, Xavier; Chéritat, Arnaud 18 2004 Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles. Zbl 1201.37032Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe 17 2010 Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow. Zbl 1287.58016Avila, Artur; Gouëzel, Sébastien 17 2013 A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019Avila, Artur; Bochi, Jairo 17 2002 Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001Avila, Artur; Viana, Marcelo 15 2007 Symplectic and isometric \(\mathrm{SL}(2,\mathbb{R})\)-invariant subbundles of the Hodge bundle. Zbl 1387.14093Avila, Artur; Eskin, Alex; Möller, Martin 13 2017 On the Hausdorff dimension of the Rauzy gasket. (Sur la dimension de Hausdorff de la baderne de Rauzy.) Zbl 1356.37018Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra 13 2016 Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007Avila, Artur; Bochi, Jairo; Damanik, David 13 2012 The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047Avila, Artur; Lyubich, Mikhail 12 2011 On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077Avila, Artur 11 2015 Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra 11 2016 Smoothness of solenoidal attractors. Zbl 1106.37015Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato 11 2006 Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089Avila, Artur; Damanik, David; Zhang, Zhenghe 11 2014 The visits to zero of a random walk driven by an irrational rotation. Zbl 1326.60060Avila, A.; Dolgopyat, D.; Duryev, E.; Sarig, O. 10 2015 Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna 10 2011 A generic \(C^1\) map has no absolutely continuous invariant probability measure. Zbl 1190.37018Avila, Artur; Bochi, Jairo 10 2006 On rigidity of critical circle maps. Zbl 1314.37028Avila, Artur 10 2013 Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052Avila, Artur; Kocsard, Alejandro 9 2011 Nonuniform center bunching and the genericity of ergodicity among \(C^1\) partially hyperbolic symplectomorphisms. Zbl 1191.37017Avila, Artur; Bochi, Jairo; Wilkinson, Amie 8 2009 Cocycles over partially hyperbolic maps. Zbl 1350.37004Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie 8 2013 \(C^1\) density of stable ergodicity. Zbl 1458.37048Avila, A.; Crovisier, S.; Wilkinson, A. 8 2021 Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan 7 2018 Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025Avila, Artur; Jitomirskaya, Svetlana 7 2011 Statistical properties of unimodal maps. Zbl 1078.37030Avila, Artur; Moreira, Carlos Gustavo 7 2005 Solving the Ten Martini problem. Zbl 1166.47303Avila, Artur; Jitomirskaya, Svetlana 7 2006 Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005Avila, Artur; Delecroix, Vincent 7 2016 Robust transitivity and topological mixing for \(C^1\)-flows. Zbl 1040.37013Abdenur, Flavio; Avila, Artur; Bochi, Jairo 7 2004 Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021Avila, Artur; Moreira, Carlos Gustavo 7 2003 Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045Avila, Artur; Lyubich, Mikhail 7 2006 Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 6 2018 Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033Avila, Artur; Resende, Maria João 6 2012 \(\mathrm{SL}(2,\mathbb R)\)-invariant probability measures on the moduli spaces of translation surfaces are regular. Zbl 1316.37016Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 6 2013 A uniform dichotomy for generic \(\mathrm{SL}(2,\mathbb R)\) cocycles over a minimal base. Zbl 1217.37017Avila, Artur; Bochi, Jairo 6 2007 Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076Avila, Artur; Lyubich, Mikhail; Shen, Weixiao 5 2011 Infinitesimal perturbations of rational maps. Zbl 1073.37051Avila, Artur 5 2002 Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004Avila, Artur; Bufetov, Alexander 5 2007 Density of positive Lyapunov exponents for quasiperiodic SL\((2, \mathbb R)\)-cocycles in arbitrary dimension. Zbl 1191.34051Avila, Artur 4 2009 On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015Avila, Artur; Fayad, Bassam; Kocsard, Alejandro 4 2015 Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012Avila, Artur; Candela, Pablo 4 2016 Recurrence for the wind-tree model. Zbl 1436.37006Avila, A.; Hubert, P. 4 2020 Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022Avila, Artur; Moreira, Carlos Gustavo 4 2005 Convergence of an exact quantization scheme. Zbl 1068.81041Avila, Artur 3 2004 Some monoids of Pisot matrices. Zbl 1445.15016Avila, Artur; Delecroix, Vincent 3 2019 Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014Avila, Artur; Viana, Marcelo 3 2005 Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059Avila, Artur; Cheraghi, Davoud 2 2018 Weak mixing properties of interval exchange transformations & translation flows. (Propriétés de mélange faible des échanges d’intervalles et des flots de translation.) Zbl 1402.37002Avila, Artur; Leguil, Martin 2 2018 Second phase transition line. Zbl 1416.37010Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi 2 2018 The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 2 2019 Bifurcations of unimodal maps. Zbl 1070.37018Avila, Artur; Moreira, Carlos Gustavo 2 2003 Uniform exponential growth for some \(SL(2,\mathbb R)\) matrix products. Zbl 1189.37060Avila, Artur; Roblin, Thomas 2 2009 Cocycles over partially hyperbolic maps. Zbl 1417.37004Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie 2 2013 Generic expanding maps without absolutely continuous invariant \(\sigma\)-finite measure. Zbl 1139.28005Avila, Artur; Bochi, Jairo 2 2007 Dynamics of renormalization operators. Zbl 1252.37030Avila, Artur 2 2011 On mixing diffeomorphisms of the disc. Zbl 1448.37052Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan 2 2020 Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028Avila, Artur 1 2002 Non-differentiable irrational curves for \(C^1\) twist map. Zbl 07457813Avila, Artur; Fayad, Bassam 1 2022 Stable accessibility with \(2\) dimensional center. Zbl 1472.37033Avila, Artur; Viana, Marcelo 1 2020 Non-differentiable irrational curves for \(C^1\) twist map. Zbl 07457813Avila, Artur; Fayad, Bassam 1 2022 \(C^1\) density of stable ergodicity. Zbl 1458.37048Avila, A.; Crovisier, S.; Wilkinson, A. 8 2021 Recurrence for the wind-tree model. Zbl 1436.37006Avila, A.; Hubert, P. 4 2020 On mixing diffeomorphisms of the disc. Zbl 1448.37052Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan 2 2020 Stable accessibility with \(2\) dimensional center. Zbl 1472.37033Avila, Artur; Viana, Marcelo 1 2020 Some monoids of Pisot matrices. Zbl 1445.15016Avila, Artur; Delecroix, Vincent 3 2019 The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 2 2019 Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan 7 2018 Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 6 2018 Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059Avila, Artur; Cheraghi, Davoud 2 2018 Weak mixing properties of interval exchange transformations & translation flows. (Propriétés de mélange faible des échanges d’intervalles et des flots de translation.) Zbl 1402.37002Avila, Artur; Leguil, Martin 2 2018 Second phase transition line. Zbl 1416.37010Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi 2 2018 Sharp phase transitions for the almost Mathieu operator. Zbl 06803180Avila, Artur; You, Jiangong; Zhou, Qi 21 2017 Spectral theory of extended Harper’s model and a question by Erdős and Szekeres. Zbl 1380.37019Avila, A.; Jitomirskaya, S.; Marx, C. A. 19 2017 Symplectic and isometric \(\mathrm{SL}(2,\mathbb{R})\)-invariant subbundles of the Hodge bundle. Zbl 1387.14093Avila, Artur; Eskin, Alex; Möller, Martin 13 2017 An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim 25 2016 Diffeomorphisms with positive metric entropy. Zbl 1362.37017Avila, A.; Crovisier, S.; Wilkinson, A. 19 2016 On the Hausdorff dimension of the Rauzy gasket. (Sur la dimension de Hausdorff de la baderne de Rauzy.) Zbl 1356.37018Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra 13 2016 Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra 11 2016 Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005Avila, Artur; Delecroix, Vincent 7 2016 Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012Avila, Artur; Candela, Pablo 4 2016 Global theory of one-frequency Schrödinger operators. Zbl 1360.37072Avila, Artur 48 2015 Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084Avila, Artur; Viana, Marcelo; Wilkinson, Amie 22 2015 Monotonic cocycles. Zbl 1356.37070Avila, Artur; Krikorian, Raphaël 19 2015 On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077Avila, Artur 11 2015 The visits to zero of a random walk driven by an irrational rotation. Zbl 1326.60060Avila, A.; Dolgopyat, D.; Duryev, E.; Sarig, O. 10 2015 On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015Avila, Artur; Fayad, Bassam; Kocsard, Alejandro 4 2015 Complex one-frequency cocycles. Zbl 1351.37136Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian 22 2014 Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089Avila, Artur; Damanik, David; Zhang, Zhenghe 11 2014 Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005Avila, Artur; Santamaria, Jimmy; Viana, Marcelo 23 2013 Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow. Zbl 1287.58016Avila, Artur; Gouëzel, Sébastien 17 2013 On rigidity of critical circle maps. Zbl 1314.37028Avila, Artur 10 2013 Cocycles over partially hyperbolic maps. Zbl 1350.37004Avila, 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 1316.37016Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe 6 2013 Cocycles over partially hyperbolic maps. Zbl 1417.37004Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie 2 2013 Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022Avila, Artur; Bochi, Jairo 19 2012 Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007Avila, Artur; Bochi, Jairo; Damanik, David 13 2012 Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033Avila, Artur; Resende, Maria João 6 2012 A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies. Zbl 1277.37089Avila, Artur; Fayad, Bassam; Krikorian, Raphaël 50 2011 Density of positive Lyapunov exponents for \(\text{SL}(2,\mathbb R)\)-cocycles. Zbl 1236.37031Avila, Artur 21 2011 The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047Avila, Artur; Lyubich, Mikhail 12 2011 Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna 10 2011 Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052Avila, Artur; Kocsard, Alejandro 9 2011 Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025Avila, Artur; Jitomirskaya, Svetlana 7 2011 Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076Avila, Artur; Lyubich, Mikhail; Shen, Weixiao 5 2011 Dynamics of renormalization operators. Zbl 1252.37030Avila, Artur 2 2011 Almost localization and almost reducibility. Zbl 1185.47028Avila, Artur; Jitomirskaya, Svetlana 62 2010 Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054Avila, Artur; Viana, Marcelo 54 2010 Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum. Zbl 1225.26031Avila, Artur; Last, Yoram; Simon, Barry 26 2010 On the regularization of conservative maps. Zbl 1211.37029Avila, Artur 24 2010 Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles. Zbl 1201.37032Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe 17 2010 The Ten Martini problem. Zbl 1166.47031Avila, Artur; Jitomirskaya, Svetlana 102 2009 On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023Avila, Artur 25 2009 Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012Avila, Artur; Bochi, Jairo; Damanik, David 20 2009 Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao 19 2009 Nonuniform center bunching and the genericity of ergodicity among \(C^1\) partially hyperbolic symplectomorphisms. Zbl 1191.37017Avila, Artur; Bochi, Jairo; Wilkinson, Amie 8 2009 Density of positive Lyapunov exponents for quasiperiodic SL\((2, \mathbb R)\)-cocycles in arbitrary dimension. Zbl 1191.34051Avila, Artur 4 2009 Uniform exponential growth for some \(SL(2,\mathbb R)\) matrix products. Zbl 1189.37060Avila, Artur; Roblin, Thomas 2 2009 Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058Avila, Artur; Lyubich, Mikhail 24 2008 Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Zbl 1149.47021Avila, Artur; Damanik, David 21 2008 Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003Avila, Artur; Forni, Giovanni 63 2007 Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001Avila, Artur; Viana, Marcelo 55 2007 Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001Avila, Artur; Viana, Marcelo 15 2007 A uniform dichotomy for generic \(\mathrm{SL}(2,\mathbb R)\) cocycles over a minimal base. Zbl 1217.37017Avila, Artur; Bochi, Jairo 6 2007 Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004Avila, Artur; Bufetov, Alexander 5 2007 Generic expanding maps without absolutely continuous invariant \(\sigma\)-finite measure. Zbl 1139.28005Avila, Artur; Bochi, Jairo 2 2007 Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033Avila, Artur; Krikorian, Raphaël 80 2006 Exponential mixing for the Teichmüller flow. Zbl 1263.37051Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe 62 2006 Smoothness of solenoidal attractors. Zbl 1106.37015Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato 11 2006 A generic \(C^1\) map has no absolutely continuous invariant probability measure. Zbl 1190.37018Avila, Artur; Bochi, Jairo 10 2006 Solving the Ten Martini problem. Zbl 1166.47303Avila, Artur; Jitomirskaya, Svetlana 7 2006 Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045Avila, Artur; Lyubich, Mikhail 7 2006 Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012Avila, Artur; Damanik, David 21 2005 Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029Avila, Artur; Moreira, Carlos Gustavo 19 2005 Statistical properties of unimodal maps. Zbl 1078.37030Avila, Artur; Moreira, Carlos Gustavo 7 2005 Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022Avila, Artur; Moreira, Carlos Gustavo 4 2005 Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014Avila, Artur; Viana, Marcelo 3 2005 Siegel disks with smooth boundaries. Zbl 1076.37030Avila, Artur; Buff, Xavier; Chéritat, Arnaud 18 2004 Robust transitivity and topological mixing for \(C^1\)-flows. Zbl 1040.37013Abdenur, Flavio; Avila, Artur; Bochi, Jairo 7 2004 Convergence of an exact quantization scheme. Zbl 1068.81041Avila, Artur 3 2004 Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018Avila, Artur; Lyubich, Mikhail; de Melo, Welington 35 2003 Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021Avila, Artur; Moreira, Carlos Gustavo 7 2003 Bifurcations of unimodal maps. Zbl 1070.37018Avila, Artur; Moreira, Carlos Gustavo 2 2003 A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019Avila, Artur; Bochi, Jairo 17 2002 Infinitesimal perturbations of rational maps. Zbl 1073.37051Avila, Artur 5 2002 Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028Avila, Artur 1 2002 all cited Publications top 5 cited Publications 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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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