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Avila Cordeiro de Melo, Artur

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Author ID: avila.artur Recent zbMATH articles by "Avila Cordeiro de Melo, Artur"
Published as: Avila, A.; Avila, Artur
Homepage: http://w3.impa.br/~avila/
External Links: MGP · Wikidata · GND
Awards: Clay Research Award (2006) · EMS Prize (2008) · Fields Medal (2014)
Documents Indexed: 92 Publications since 2001, including 1 Book
Biographic References: 8 Publications

Publications by Year

Citations contained in zbMATH Open

82 Publications have been cited 1,253 times in 751 Documents Cited by Year
The Ten Martini problem. Zbl 1166.47031
Avila, Artur; Jitomirskaya, Svetlana
91
2009
Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Zbl 1138.47033
Avila, Artur; Krikorian, Raphaël
73
2006
Almost localization and almost reducibility. Zbl 1185.47028
Avila, Artur; Jitomirskaya, Svetlana
60
2010
Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003
Avila, Artur; Forni, Giovanni
60
2007
Exponential mixing for the Teichmüller flow. Zbl 1263.37051
Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe
54
2006
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001
Avila, Artur; Viana, Marcelo
52
2007
A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
45
2011
Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054
Avila, Artur; Viana, Marcelo
45
2010
Global theory of one-frequency Schrödinger operators. Zbl 1360.37072
Avila, Artur
41
2015
Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018
Avila, Artur; Lyubich, Mikhail; de Melo, Welington
31
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
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
21
2010
Generic singular spectrum for ergodic Schrödinger operators. Zbl 1102.82012
Avila, Artur; Damanik, David
21
2005
Sharp phase transitions for the almost Mathieu operator. Zbl 06803180
Avila, Artur; You, Jiangong; Zhou, Qi
20
2017
An integrable deformation of an ellipse of small eccentricity is an ellipse. Zbl 1379.37104
Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim
20
2016
Density of positive Lyapunov exponents for \(\text{SL}(2,\mathbb R)\)-cocycles. Zbl 1236.37031
Avila, Artur
20
2011
Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058
Avila, Artur; Lyubich, Mikhail
20
2008
Complex one-frequency cocycles. Zbl 1351.37136
Avila, Artur; Jitomirskaya, Svetlana; Sadel, Christian
19
2014
Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo
19
2013
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Zbl 1165.37012
Avila, Artur; Bochi, Jairo; Damanik, David
19
2009
Statistical properties of unimodal maps: The quadratic family. Zbl 1078.37029
Avila, Artur; Moreira, Carlos Gustavo
19
2005
Monotonic cocycles. Zbl 1356.37070
Avila, Artur; Krikorian, Raphaël
18
2015
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
18
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
18
2008
Siegel disks with smooth boundaries. Zbl 1076.37030
Avila, Artur; Buff, Xavier; Chéritat, Arnaud
17
2004
Diffeomorphisms with positive metric entropy. Zbl 1362.37017
Avila, A.; Crovisier, S.; Wilkinson, A.
16
2016
Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084
Avila, Artur; Viana, Marcelo; Wilkinson, Amie
16
2015
Spectral theory of extended Harper’s model and a question by Erdős and Szekeres. Zbl 1380.37019
Avila, A.; Jitomirskaya, S.; Marx, C. A.
15
2017
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022
Avila, Artur; Bochi, Jairo
15
2012
A formula with some applications to the theory of Lyapunov exponents. Zbl 1022.37019
Avila, Artur; Bochi, Jairo
15
2002
Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001
Avila, Artur; Viana, Marcelo
14
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
Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles. Zbl 1201.37032
Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe
13
2010
On the Hausdorff dimension of the Rauzy gasket. Zbl 1356.37018
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
11
2016
On the Kotani-Last and Schrödinger conjectures. Zbl 1325.47077
Avila, Artur
11
2015
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
11
2013
Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007
Avila, Artur; Bochi, Jairo; Damanik, David
11
2012
Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
10
2016
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
10
2014
On rigidity of critical circle maps. Zbl 1314.37028
Avila, Artur
10
2013
The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047
Avila, Artur; Lyubich, Mikhail
10
2011
Smoothness of solenoidal attractors. Zbl 1106.37015
Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato
10
2006
The visits to zero of a random walk driven by an irrational rotation. Zbl 1326.60060
Avila, A.; Dolgopyat, D.; Duryev, E.; Sarig, O.
9
2015
Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012
Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna
9
2011
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
A generic \(C^1\) map has no absolutely continuous invariant probability measure. Zbl 1190.37018
Avila, Artur; Bochi, Jairo
8
2006
Weak mixing directions in non-arithmetic Veech surfaces. Zbl 1373.37005
Avila, Artur; Delecroix, Vincent
7
2016
Statistical properties of unimodal maps. Zbl 1078.37030
Avila, Artur; Moreira, Carlos Gustavo
7
2005
Livšic theorem for diffeomorphism cocycles. Zbl 1420.37033
Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan
6
2018
Cocycles over partially hyperbolic maps. Zbl 1350.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
6
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
A uniform dichotomy for generic \(\mathrm{SL}(2,\mathbb R)\) cocycles over a minimal base. Zbl 1217.37017
Avila, Artur; Bochi, Jairo
6
2007
Solving the Ten Martini problem. Zbl 1166.47303
Avila, Artur; Jitomirskaya, Svetlana
6
2006
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
6
2006
Robust transitivity and topological mixing for \(C^1\)-flows. Zbl 1040.37013
Abdenur, Flavio; Avila, Artur; Bochi, Jairo
6
2004
Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021
Avila, Artur; Moreira, Carlos Gustavo
6
2003
Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
5
2018
Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Zbl 1215.47025
Avila, Artur; Jitomirskaya, Svetlana
5
2011
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
5
2011
Density of positive Lyapunov exponents for quasiperiodic SL\((2, \mathbb R)\)-cocycles in arbitrary dimension. Zbl 1191.34051
Avila, Artur
5
2009
On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Zbl 1316.37015
Avila, Artur; Fayad, Bassam; Kocsard, Alejandro
4
2015
Exponential decay of correlations for the Rauzy-Veech-Zorich induction map. Zbl 1149.37004
Avila, Artur; Bufetov, Alexander
4
2007
Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Zbl 1145.37022
Avila, Artur; Moreira, Carlos Gustavo
4
2005
Cocycles over partially hyperbolic maps. Zbl 1417.37004
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie
3
2013
Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033
Avila, Artur; Resende, Maria João
3
2012
Dynamics in the moduli space of Abelian differentials. Zbl 1087.14014
Avila, Artur; Viana, Marcelo
3
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
2
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
Weak mixing properties of interval exchange transformations & translation flows. Zbl 1402.37002
Avila, Artur; Leguil, Martin
2
2018
Second phase transition line. Zbl 1416.37010
Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi
2
2018
Dynamics of renormalization operators. Zbl 1252.37030
Avila, Artur
2
2011
Uniform exponential growth for some \(SL(2,\mathbb R)\) matrix products. Zbl 1189.37060
Avila, Artur; Roblin, Thomas
2
2009
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
Recurrence for the wind-tree model. Zbl 1436.37006
Avila, A.; Hubert, P.
1
2020
Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059
Avila, Artur; Cheraghi, Davoud
1
2018
Towers for commuting endomorphisms, and combinatorial applications. Zbl 1360.28012
Avila, Artur; Candela, Pablo
1
2016
Infinitesimal perturbations of rational maps. Zbl 1073.37051
Avila, Artur
1
2002
Bifurcation of unimodal maps. Zbl 1015.37028
Avila, Artur
1
2002
Recurrence for the wind-tree model. Zbl 1436.37006
Avila, A.; Hubert, P.
1
2020
Some monoids of Pisot matrices. Zbl 1445.15016
Avila, Artur; Delecroix, Vincent
2
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
6
2018
Zorich conjecture for hyperelliptic Rauzy-Veech groups. Zbl 1381.05088
Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe
5
2018
Weak mixing properties of interval exchange transformations & translation flows. Zbl 1402.37002
Avila, Artur; Leguil, Martin
2
2018
Second phase transition line. Zbl 1416.37010
Avila, Artur; Jitomirskaya, Svetlana; Zhou, Qi
2
2018
Statistical properties of quadratic polynomials with a neutral fixed point. Zbl 1402.37059
Avila, Artur; Cheraghi, Davoud
1
2018
Sharp phase transitions for the almost Mathieu operator. Zbl 06803180
Avila, Artur; You, Jiangong; Zhou, Qi
20
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.
15
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
20
2016
Diffeomorphisms with positive metric entropy. Zbl 1362.37017
Avila, A.; Crovisier, S.; Wilkinson, A.
16
2016
On the Hausdorff dimension of the Rauzy gasket. Zbl 1356.37018
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
11
2016
Diffusion for chaotic plane sections of 3-periodic surfaces. Zbl 1376.37030
Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
10
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. Zbl 1360.28012
Avila, Artur; Candela, Pablo
1
2016
Global theory of one-frequency Schrödinger operators. Zbl 1360.37072
Avila, Artur
41
2015
Monotonic cocycles. Zbl 1356.37070
Avila, Artur; Krikorian, Raphaël
18
2015
Absolute continuity, Lyapunov exponents and rigidity. I: Geodesic flows. Zbl 1352.37084
Avila, Artur; Viana, Marcelo; Wilkinson, Amie
16
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.
9
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
19
2014
Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Zbl 1303.47089
Avila, Artur; Damanik, David; Zhang, Zhenghe
10
2014
Holonomy invariance: rough regularity and applications to Lyapunov exponents. Zbl 1348.37005
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo
19
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
11
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
6
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
3
2013
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Zbl 1257.37022
Avila, Artur; Bochi, Jairo
15
2012
Opening gaps in the spectrum of strictly ergodic Schrödinger operators. Zbl 1263.37007
Avila, Artur; Bochi, Jairo; Damanik, David
11
2012
Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Zbl 1267.37033
Avila, Artur; Resende, Maria João
3
2012
A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies. Zbl 1277.37089
Avila, Artur; Fayad, Bassam; Krikorian, Raphaël
45
2011
Density of positive Lyapunov exponents for \(\text{SL}(2,\mathbb R)\)-cocycles. Zbl 1236.37031
Avila, Artur
20
2011
The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047
Avila, Artur; Lyubich, Mikhail
10
2011
Mixing for the time-changes of Heisenberg nilflows. Zbl 1281.37012
Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna
9
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
5
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
60
2010
Extremal Lyapunov exponents: an invariance principle and applications. Zbl 1196.37054
Avila, Artur; Viana, Marcelo
45
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
21
2010
Uniformly hyperbolic finite-valued \(\mathrm{SL}(2,\mathbb R)\)-cocycles. Zbl 1201.37032
Avila, Artur; Bochi, Jairo; Yoccoz, Jean-Christophe
13
2010
The Ten Martini problem. Zbl 1166.47031
Avila, Artur; Jitomirskaya, Svetlana
91
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
19
2009
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
18
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
5
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
20
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
18
2008
Weak mixing for interval exchange transformations and translation flows. Zbl 1136.37003
Avila, Artur; Forni, Giovanni
60
2007
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Zbl 1143.37001
Avila, Artur; Viana, Marcelo
52
2007
Simplicity of Lyapunov spectra: a sufficient criterion. Zbl 1137.37001
Avila, Artur; Viana, Marcelo
14
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
4
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
73
2006
Exponential mixing for the Teichmüller flow. Zbl 1263.37051
Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe
54
2006
Smoothness of solenoidal attractors. Zbl 1106.37015
Avila, Artur; Gouëzel, Sébastien; Tsujii, Masato
10
2006
A generic \(C^1\) map has no absolutely continuous invariant probability measure. Zbl 1190.37018
Avila, Artur; Bochi, Jairo
8
2006
Solving the Ten Martini problem. Zbl 1166.47303
Avila, Artur; Jitomirskaya, Svetlana
6
2006
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
6
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
17
2004
Robust transitivity and topological mixing for \(C^1\)-flows. Zbl 1040.37013
Abdenur, Flavio; Avila, Artur; Bochi, Jairo
6
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
31
2003
Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative. Zbl 1046.37021
Avila, Artur; Moreira, Carlos Gustavo
6
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
15
2002
Infinitesimal perturbations of rational maps. Zbl 1073.37051
Avila, Artur
1
2002
Bifurcation of unimodal maps. Zbl 1015.37028
Avila, Artur
1
2002
all top 5

Cited by 724 Authors

44 Avila Cordeiro de Melo, Artur
31 Damanik, David
24 Jitomirskaya, Svetlana Ya.
14 You, Jiangong
13 Bochi, Jairo
13 Viana, Marcelo
13 Zhou, Qi
12 Fillman, Jake
12 Matheus, Carlos
11 Liu, Wencai
10 Gorodetski, Anton
10 Ulcigrai, Corinna
9 Bessa, Mário
9 Breuer, Jonathan
9 Yang, Jiagang
9 Yoccoz, Jean-Christophe
8 Araújo, Vítor
8 Varandas, Paulo
8 Xu, Junxiang
7 Bufetov, Aleksandr Igorevich
7 Chaika, Jonathan
7 Crovisier, Sylvain
7 Eskin, Alex
7 Forni, Giovanni
7 Han, Rui
7 Krüger, Helge
7 Lubinsky, Doron S.
7 Lyubich, Mikhail Yur’evich
7 Rodriguez-Hertz, Federico
7 Yuan, Xiaoping
7 Zhang, Dongfeng
7 Zhao, Xin
6 Bjerklöv, Kristian
6 Butterley, Oliver
6 de Melo, Welington
6 Ferenczi, Sébastien
6 Hou, Xuanji
6 Hubert, Pascal
6 Masur, Howard A.
6 Rempe-Gillen, Lasse
6 Tahzibi, Ali
6 Wilkinson, Amie
6 Wright, Alex
5 Backes, Lucas H.
5 Baladi, Viviane
5 Bruin, Henk
5 Gan, Zheng
5 Gelfert, Katrin Grit
5 Goldstein, Michael
5 Gouëzel, Sébastien
5 Guarino, Pablo
5 Oertel-Jäger, Tobias Hendrik
5 Kaloshin, Vadim Yu.
5 Kanigowski, Adam
5 Kocsard, Alejandro
5 Last, Yoram
5 Marx, Christoph A.
5 Melbourne, Ian
5 Mirzakhani, Maryam
5 Poletti, Mauricio
5 Rams, Michał
5 Rodriguez Hertz, Jana
5 Sadovskaya, Victoria
5 Shen, Weixiao
5 van Strien, Sebastian J.
5 Xu, Disheng
5 Yang, Fan
5 Zhang, Zhiyuan
4 Bialy, Misha
4 Boissy, Corentin
4 Buff, Xavier
4 Carrasco, Pablo D.
4 Chéritat, Arnaud
4 Iommi, Godofredo
4 Khanin, Konstantin M.
4 Kocić, Saša
4 Liverani, Carlangelo
4 Lukic, Milivoje
4 Morris, Ian D.
4 Ong, Darren C.
4 Qu, Yanhui
4 Ravotti, Davide
4 Rocha, Jorge
4 Si, Jianguo
4 Skripchenko, Alexandra
4 Smania, Daniel
4 Solomyak, Boris
4 Tao, Kai
4 Todd, Mike
4 Yampolsky, Michael
4 Zhang, Shiwen
3 Alpan, Gökalp
3 Apisa, Paul
3 Athreya, Jayadev S.
3 Aulicino, David
3 Bárány, Balázs
3 Berger, Pierre
3 Berthé, Valérie
3 Bonatti, Christian
3 Boshernitzan, Michael D.
...and 624 more Authors
all top 5

Cited in 153 Serials

69 Communications in Mathematical Physics
64 Ergodic Theory and Dynamical Systems
29 Inventiones Mathematicae
25 Proceedings of the American Mathematical Society
25 Discrete and Continuous Dynamical Systems
24 Journal of Functional Analysis
21 Advances in Mathematics
19 Journal of Modern Dynamics
17 Annals of Mathematics. Second Series
17 Journal of the European Mathematical Society (JEMS)
16 Transactions of the American Mathematical Society
15 Geometric and Functional Analysis. GAFA
14 Duke Mathematical Journal
13 Israel Journal of Mathematics
13 Nonlinearity
12 Journal of Mathematical Physics
11 Journal d’Analyse Mathématique
10 Journal of Statistical Physics
10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
10 Journal of the American Mathematical Society
10 Journal of Dynamics and Differential Equations
9 Journal of Differential Equations
9 Journal of Spectral Theory
8 Journal of Mathematical Analysis and Applications
8 Annales de l’Institut Fourier
8 Mathematische Zeitschrift
8 Annales Henri Poincaré
7 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 Acta Mathematica
5 Constructive Approximation
5 Journal of Difference Equations and Applications
4 Letters in Mathematical Physics
4 Mathematical Proceedings of the Cambridge Philosophical Society
4 Commentarii Mathematici Helvetici
4 Journal of Approximation Theory
4 Monatshefte für Mathematik
4 Mathematical Physics, Analysis and Geometry
4 Dynamical Systems
4 Journal of the Institute of Mathematics of Jussieu
4 Frontiers of Mathematics in China
3 Annali di Matematica Pura ed Applicata. Serie Quarta
3 Memoirs of the American Mathematical Society
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 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
3 Experimental Mathematics
3 Geometry & Topology
3 Qualitative Theory of Dynamical Systems
3 Discrete and Continuous Dynamical Systems. Series B
3 Portugaliae Mathematica. Nova Série
2 Indian Journal of Pure & Applied Mathematics
2 Mathematical Notes
2 Russian Mathematical Surveys
2 Bulletin de la Société Mathématique de France
2 Mathematische Nachrichten
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Probability Theory and Related Fields
2 Bulletin of the American Mathematical Society. New Series
2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
2 Indagationes Mathematicae. New Series
2 Conformal Geometry and Dynamics
2 Regular and Chaotic Dynamics
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Stochastics and Dynamics
2 Communications on Pure and Applied Analysis
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 Proceedings of the Steklov Institute of Mathematics
2 Journal of Physics A: Mathematical and Theoretical
2 Discrete and Continuous Dynamical Systems. Series S
2 Science China. Mathematics
2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Applicable Analysis
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 Compositio Mathematica
1 Dissertationes Mathematicae
1 Functional Analysis and its Applications
1 Integral Equations and Operator Theory
1 Journal of Differential Geometry
1 Journal of the London Mathematical Society. Second Series
1 Journal für die Reine und Angewandte Mathematik
1 Michigan Mathematical Journal
1 Osaka Journal of Mathematics
1 Pacific Journal of Mathematics
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Theoretical Computer Science
...and 53 more Serials
all top 5

Cited in 46 Fields

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

Citations by Year

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