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Author ID: avila.artur Recent zbMATH articles by "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)

Publications by Year

Citations contained in zbMATH Open

94 Publications have been cited 2,079 times in 1,190 Documents Cited by Year
The Ten Martini problem. Zbl 1166.47031
Avila, Artur; Jitomirskaya, Svetlana
142
2009
Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033
Avila, Artur; Krikorian, Raphaël
113
2006
Exponential mixing for the Teichmüller flow. Zbl 1263.37051
Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe
96
2006
Almost localization and almost reducibility. Zbl 1185.47028
Avila, Artur; Jitomirskaya, Svetlana
89
2010
A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
87
2011
Global theory of one-frequency Schrödinger operators. Zbl 1360.37072
Avila, Artur
85
2015
Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054
Avila, Artur; Viana, Marcelo
84
2010
Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003
Avila, Artur; Forni, Giovanni
83
2007
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
49
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.
37
2017
Complex one-frequency cocycles. Zbl 1351.37136
Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian
34
2014
Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo
32
2013
On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023
Avila, Artur
31
2009
Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084
Avila, Artur; Viana, Marcelo; Wilkinson, Amie
30
2015
Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058
Avila, Artur; Lyubich, Mikhail
30
2008
Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles. Zbl 1201.37032
Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe
30
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
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012
Avila, Artur; Bochi, Jairo; Damanik, David
28
2009
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
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
28
2009
Diffeomorphisms with positive metric entropy. Zbl 1362.37017
Avila, A.; Crovisier, S.; Wilkinson, A.
27
2016
Monotonic cocycles. Zbl 1356.37070
Avila, Artur; Krikorian, Raphaël
26
2015
Density of positive Lyapunov exponents for \(\text{SL}(2,\mathbb R)\)-cocycles. Zbl 1236.37031
Avila, Artur
26
2011
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
Siegel disks with smooth boundaries. Zbl 1076.37030
Avila, Artur; Buff, Xavier; Chéritat, Arnaud
24
2004
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
24
2013
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
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022
Avila, Artur; Bochi, Jairo
22
2012
\(C^1\) density of stable ergodicity. Zbl 1458.37048
Avila, A.; Crovisier, S.; Wilkinson, A.
22
2021
A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019
Avila, Artur; Bochi, Jairo
21
2002
Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001
Avila, Artur; Viana, Marcelo
21
2007
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
18
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
Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005
Avila, Artur; Delecroix, Vincent
16
2016
Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
15
2016
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
15
2014
Smoothness of solenoidal attractors. Zbl 1106.37015
Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato
15
2006
On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077
Avila, Artur
14
2015
Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052
Avila, Artur; Kocsard, Alejandro
14
2011
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
A generic \(C^1\) map has no absolutely continuous invariant probability measure. Zbl 1190.37018
Avila, Artur; Bochi, Jairo
12
2006
Recurrence for the wind-tree model. Zbl 1436.37006
Avila, A.; Hubert, P.
12
2020
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
11
2011
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
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
Second phase transition line. Zbl 1416.37010
Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi
9
2018
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
9
2006
Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021
Avila, Artur; Moreira, Carlos Gustavo
9
2003
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
Solving the Ten Martini problem. Zbl 1166.47303
Avila, Artur; Jitomirskaya, Svetlana
8
2006
Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
7
2018
\(\mathrm{SL}(2,\mathbb R)\)-invariant probability measures on the moduli spaces of translation surfaces are regular. Zbl 1316.37016
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
7
2013
A uniform dichotomy for generic \(\mathrm{SL}(2,\mathbb R)\) cocycles over a minimal base. Zbl 1217.37017
Avila, Artur; Bochi, Jairo
7
2007
Statistical properties of unimodal maps. Zbl 1078.37030
Avila, Artur; Moreira, Carlos Gustavo
7
2005
Robust transitivity and topological mixing for \(C^1\)-flows. Zbl 1040.37013
Abdenur, Flavio; Avila, Artur; Bochi, Jairo
7
2004
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
Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004
Avila, Artur; Bufetov, Alexander
6
2007
Absolute continuity, Lyapunov exponents, and rigidity. II: Systems with compact center leaves. Zbl 1493.37022
Avila, A.; Viana, Marcelo; Wilkinson, A.
6
2022
Infinitesimal perturbations of rational maps. Zbl 1073.37051
Avila, Artur
5
2002
Towers for commuting endomorphisms, and combinatorial applications. (Tours pour endomorphismes commutants, et applications combinatoires.) Zbl 1360.28012
Avila, Artur; Candela, Pablo
5
2016
Density of positive Lyapunov exponents for quasiperiodic SL\((2, \mathbb R)\)-cocycles in arbitrary dimension. Zbl 1191.34051
Avila, Artur
5
2009
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
Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059
Avila, Artur; Cheraghi, Davoud
5
2018
Schrödinger operators with potentials generated by hyperbolic transformations. I: Positivity of the Lyapunov exponent. Zbl 1511.37038
Avila, Artur; Damanik, David; Zhang, Zhenghe
5
2023
On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015
Avila, Artur; Fayad, Bassam; Kocsard, Alejandro
4
2015
The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces. Zbl 1426.37030
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
4
2019
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
Dynamics of renormalization operators. Zbl 1252.37030
Avila, Artur
3
2011
Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014
Avila, Artur; Viana, Marcelo
3
2005
Uniform exponential growth for some \(SL(2,\mathbb R)\) matrix products. Zbl 1189.37060
Avila, Artur; Roblin, Thomas
3
2009
On mixing diffeomorphisms of the disc. Zbl 1448.37052
Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
3
2020
Cocycles over partially hyperbolic maps. Zbl 1417.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
2
2013
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
Invariant graphs and spectral type of Schrödinger operators. Zbl 1472.35106
Avila, Artur; Khanin, Konstantin; Leguil, Martin
2
2020
The spectrum of Schrödinger operators with randomly perturbed ergodic potentials. Zbl 07680038
Avila, Artur; Damanik, David; Gorodetski, Anton
2
2023
Stable accessibility with \(2\) dimensional center. Zbl 1472.37033
Avila, Artur; Viana, Marcelo
2
2020
Bifurcation of unimodal maps. (Bifurcations d’applications unimodales.) Zbl 1015.37028
Avila, Artur
1
2002
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
Non-differentiable irrational curves for \(C^1\) twist map. Zbl 1490.37057
Avila, Artur; Fayad, Bassam
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
5
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.
6
2022
Analytic maps of parabolic and elliptic type with trivial centralisers. Zbl 1512.37051
Avila, Artur; Cheraghi, Davoud; Eliad, Alexander
1
2022
Non-differentiable irrational curves for \(C^1\) twist map. Zbl 1490.37057
Avila, Artur; Fayad, Bassam
1
2022
\(C^1\) density of stable ergodicity. Zbl 1458.37048
Avila, A.; Crovisier, S.; Wilkinson, A.
22
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.
12
2020
On mixing diffeomorphisms of the disc. Zbl 1448.37052
Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
3
2020
Invariant graphs and spectral type of Schrödinger operators. Zbl 1472.35106
Avila, Artur; Khanin, Konstantin; Leguil, Martin
2
2020
Stable accessibility with \(2\) dimensional center. Zbl 1472.37033
Avila, Artur; Viana, Marcelo
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
Second phase transition line. Zbl 1416.37010
Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi
9
2018
Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033
Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan
9
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
49
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.
37
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
Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005
Avila, Artur; Delecroix, Vincent
16
2016
Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
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
85
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
26
2015
On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077
Avila, Artur
14
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 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
34
2014
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
15
2014
Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo
32
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
24
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
87
2011
Density of positive Lyapunov exponents for \(\text{SL}(2,\mathbb R)\)-cocycles. Zbl 1236.37031
Avila, Artur
26
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
18
2011
Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Zbl 1225.37052
Avila, Artur; Kocsard, Alejandro
14
2011
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
11
2011
Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025
Avila, Artur; Jitomirskaya, Svetlana
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
89
2010
Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054
Avila, Artur; Viana, Marcelo
84
2010
Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles. Zbl 1201.37032
Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe
30
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
The Ten Martini problem. Zbl 1166.47031
Avila, Artur; Jitomirskaya, Svetlana
142
2009
On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators. Zbl 1188.47023
Avila, Artur
31
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
28
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
5
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
83
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
113
2006
Exponential mixing for the Teichmüller flow. Zbl 1263.37051
Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe
96
2006
Smoothness of solenoidal attractors. Zbl 1106.37015
Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato
15
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
8
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
21
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 top 5

Cited by 1,035 Authors

51 Avila, Artur
44 Damanik, David
30 Jitomirskaya, Svetlana Yakovlevna
22 You, Jiangong
19 Fillman, Jake
19 Zhou, Qi
16 Matheus, Carlos
16 Viana, Marcelo
15 Bochi, Jairo
13 Liu, Wencai
13 Ulcigrai, Corinna
13 Yang, Jiagang
13 Zhang, Dongfeng
12 Forni, Giovanni
12 Gorodetskii, Anton Semenovich
12 Rodriguez-Hertz, Federico
11 Crovisier, Sylvain
11 Ge, Lingrui
11 Varandas, Paulo
11 Xu, Junxiang
10 Araújo, Vítor
10 Bessa, Mário
10 Cao, Yongluo
10 Gelfert, Katrin Grit
10 Guarino, Pablo
10 Hubert, Pascal
10 Kanigowski, Adam
10 Lubinsky, Doron S.
10 Lyubich, Mikhail
10 Tahzibi, Ali
10 Zhao, Xin
9 Breuer, Jonathan
9 Chaika, Jonathan
9 Sadovskaya, Victoria
9 Wang, Jing
9 Wilkinson, Amie
9 Wright, Alex
9 Yoccoz, Jean-Christophe
8 Bjerklöv, Kristian
8 Bufetov, Aleksandr Igorevich
8 Eskin, Alex
8 Han, Rui
8 Hou, Xuanji
8 Kaloshin, Vadim Yu.
8 Poletti, Mauricio
8 Pollicott, Mark
8 Zhang, Zhiyuan
7 Baladi, Viviane
7 Butterley, Oliver
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 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 Bezerra, Jamerson
6 Bruin, Henk
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
6 Zou, Rui
5 Backes, Lucas H.
5 Berthé, Valérie
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.
...and 935 more Authors
all top 5

Cited in 201 Serials

103 Ergodic Theory and Dynamical Systems
90 Communications in Mathematical Physics
41 Advances in Mathematics
40 Discrete and Continuous Dynamical Systems
36 Inventiones Mathematicae
34 Nonlinearity
31 Journal of Modern Dynamics
29 Journal of Functional Analysis
29 Proceedings of the American Mathematical Society
26 Journal of the European Mathematical Society (JEMS)
24 Journal of Mathematical Physics
24 Annals of Mathematics. Second Series
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
17 Journal of Spectral Theory
16 Israel Journal of Mathematics
16 Duke Mathematical Journal
16 Journal of Differential Equations
16 Mathematische Zeitschrift
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 Arnold Mathematical Journal
7 Journal de l’École Polytechnique – Mathématiques
6 Commentarii Mathematici Helvetici
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
5 Letters in Mathematical Physics
5 Mathematical Notes
5 Mathematical Proceedings of the Cambridge Philosophical Society
5 Acta Mathematica
5 Bulletin of the London Mathematical Society
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 Journal of Approximation Theory
4 Monatshefte für Mathematik
4 Transactions of the Moscow Mathematical Society
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 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 Discrete and Continuous Dynamical Systems. Series S
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
...and 101 more Serials
all top 5

Cited in 52 Fields

905 Dynamical systems and ergodic theory (37-XX)
183 Operator theory (47-XX)
127 Quantum theory (81-XX)
100 Ordinary differential equations (34-XX)
84 Partial differential equations (35-XX)
80 Functions of a complex variable (30-XX)
71 Measure and integration (28-XX)
71 Several complex variables and analytic spaces (32-XX)
71 Statistical mechanics, structure of matter (82-XX)
51 Probability theory and stochastic processes (60-XX)
49 Number theory (11-XX)
44 Difference and functional equations (39-XX)
41 Mechanics of particles and systems (70-XX)
31 Harmonic analysis on Euclidean spaces (42-XX)
29 Manifolds and cell complexes (57-XX)
27 Algebraic geometry (14-XX)
24 Differential geometry (53-XX)
23 Linear and multilinear algebra; matrix theory (15-XX)
23 Topological groups, Lie groups (22-XX)
20 Global analysis, analysis on manifolds (58-XX)
16 Convex and discrete geometry (52-XX)
14 Functional analysis (46-XX)
13 Computer science (68-XX)
11 Real functions (26-XX)
10 Combinatorics (05-XX)
10 General topology (54-XX)
9 Group theory and generalizations (20-XX)
9 Potential theory (31-XX)
8 Special functions (33-XX)
8 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 Algebraic topology (55-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)
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

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