×

Avila Cordeiro de Melo, Artur

Compute Distance To:
Author ID: avila.artur Recent zbMATH articles by "Avila Cordeiro de Melo, 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

Publications by Year

Citations contained in zbMATH Open

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