Papers
Published
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On the dynamics of the renormalization operator.
A. Avila, Marco Martens, Welington de Melo.
In ``Global Analysis of Dynamical Systems:
Festschrift dedicated to Floris Takens for his 60th birthday'',
Ed. H.Broer, B. Krauskopf, G. Vegter,
Institute of Physics Publishing, Bristol and
Philadelphia, pp. 449-460, 2001.
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Infinitesimal perturbations of rational maps.
Nonlinearity 15 (2002), 695-704.
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A formula with some applications to the theory of Lyapunov exponents.
A. Avila, Jairo Bochi.
Israel Journal of Mathematics 131 (2002), 125-137.
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Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative.
A. Avila, Carlos Gustavo Moreira.
Astérisque 286 (2003), 81-118.
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Regular or stochastic dynamics in real analytic families of unimodal maps.
A. Avila, Mikhail Lyubich, W. de Melo.
Inventiones Mathematicae 154 (2003), 451-550.
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Robust transitivity and topological mixing for $C^1$-flows.
Flavio Abdenur, A. Avila, J. Bochi.
Proceedings of the American Mathematical Society 132 (2004), 699-705.
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Convergence of an exact quantization scheme.
Communications in Mathematical Physics 249 (2004), 305-318.
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Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family.
A. Avila, C. G. Moreira.
Bulletin of the Brazilian Mathematical Society 35 (2004), 291-331.
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Siegel disks with smooth boundaries.
A. Avila, Xavier Buff, Arnaud Chéritat.
Acta Mathematica 193 (2004), 1-30.
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Statistical properties of unimodal maps: the quadratic family.
A. Avila, C. G. Moreira.
Annals of Mathematics 161 (2005), 831-881.
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Statistical properties of unimodal maps: physical measures, periodic
points and pathological laminations.
A. Avila, C. G. Moreira.
Publications Mathématiques de l'IHÉS 101 (2005), 1-67.
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Generic singular spectrum for ergodic Schrödinger operators.
A. Avila, David Damanik.
Duke Mathematical Journal 130 (2005), 393-400.
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Phase-Parameter relation and sharp statistical properties for
general families of unimodal maps.
A. Avila, C. G. Moreira.
Contemporary Mathematics 389 (2005), 1-42.
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Smoothness of solenoidal attractors.
A. Avila, Sébastien Gouëzel, Masato Tsujii.
Discrete and Continuous Dynamical Systems 15 (2006), 21-35.
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Examples of Feigenbaum Julia sets with small Hausdorff dimension.
A. Avila, M. Lyubich.
In ``Dynamics on the Riemann Sphere. A Bodil Branner Festschrift'',
Ed. Poul G. Hjorth, Carsten Lunde Petersen, European Mathematical
Society (EMS), Zürich, pp. 71-87, 2006.
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A generic $C^1$ map has no absolutely continuous invariant measure.
A. Avila, J. Bochi.
Nonlinearity 19 (2006), 2717-2725.
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Reducibility or non-uniform hyperbolicity for quasiperiodic
Schrödinger cocycles.
A. Avila, Raphaël Krikorian.
Annals of Mathematics 164 (2006), 911-940.
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Exponential mixing for the Teichmüller flow.
A. Avila, S. Gouëzel and
Jean-Christophe Yoccoz.
Publications Mathématiques de l'IHÉS 104 (2006), 143-211.
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Weak mixing for interval exchange transformations and translation flows.
A. Avila, Giovanni Forni.
Annals of Mathematics 165 (2007), 637-664.
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Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture.
A. Avila, Marcelo Viana.
Acta Mathematica 198 (2007), 1-56.
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Generic expanding maps without absolutely continuous invariant $\sigma$-finite measure.
A. Avila, J. Bochi.
Mathematical Research Letters 14 (2007), 721-730.
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Simplicity of Lyapunov spectra: a sufficient criterion.
A. Avila, M. Viana.
Portugaliae Mathematica 64 (2007), 311-376.
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A uniform dichotomy for generic SL(2,R) cocycles over a minimal base.
A. Avila, J. Bochi.
Bulletin de la Société Mathématique de France 135 (2007), 407-417.
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Exponential decay of correlations for the Rauzy-Veech-Zorich induction
map.
A. Avila, Alexander Bufetov.
Fields Institute Communications 51 (2007), 203-211.
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Hausdorff dimension and conformal measures of Feigenbaum Julia sets.
A. Avila, M. Lyubich.
Journal of the American Mathematical Society 21 (2008), 305-363.
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Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical
coupling.
A. Avila, D. Damanik.
Inventiones Mathematicae 172 (2008), 439-453.
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Cantor Spectrum for Schrödinger Operators with Potentials arising from Generalized
Skew-shifts.
A. Avila, J. Bochi and D. Damanik.
Duke Mathematical Journal 146 (2009), 253-280.
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On the spectrum and Lyapunov exponent of limit
periodic Schrödinger operators.
Communications in Mathematical Physics 288 (2009), 907-918.
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The Ten Martini Problem.
A. Avila, Svetlana Jitomirskaya.
Annals of Mathematics 170 (2009), 303-342.
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Combinatorial rigidity for unicritical polynomials.
A. Avila, Jeremy Kahn, M. Lyubich and Weixiao Shen.
Annals of Mathematics 170 (2009), 783-797.
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Nonuniform center bunching and the genericity of ergodicity among $C^1$
partially hyperbolic symplectomorphisms.
A. Avila, J. Bochi, Amie Wilkinson.
Annales Scientifiques de l'Ecole Normale Superieure 42 (2009),
931-979.
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Uniform exponential growth for some SL(2,R) matrix products.
A. Avila, Thomas Roblin.
Journal of Modern Dynamics 3 (2009), 549-554.
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Density of positive Lyapunov exponents for quasiperiodic SL(2,R) cocycles in arbitrary dimension.
Journal of Modern Dynamics 3 (2009), 629-634.
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Almost localization and almost reducibility.
A. Avila, S. Jitomirskaya.
Journal of the European Mathematical Society 12 (2010), 93-131.
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Extremal Lyapunov exponents: an invariance principle and
applications.
A. Avila, M. Viana.
Inventiones Mathematicae 181 (2010), 115-174.
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Bulk universality and clock spacing of zeros for ergodic Jacobi matrices
with a.c. spectrum.
A. Avila, Barry Simon, Yoram Last.
Analysis & PDE 3 (2010), 81-118.
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Uniformly hyperbolic finite-valued SL(2,R)-cocycles.
A. Avila, J. Bochi, J.-C. Yoccoz.
Commentarii Mathematici Helvetici 85 (2010), 813-884.
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On the regularization of conservative maps.
Acta Mathematica 205 (2010), 5-18.
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Parapuzzle of the Multibrot set and typical dynamics of unimodal maps.
A. Avila, M. Lyubich, W. Shen.
Journal of the European Mathematical Society 13 (2011), 27-56.
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Hölder continuity of absolutely continuous spectral measures for
one-frequency Schrödinger operators.
A. Avila, S. Jitomirskaya.
Communications in Mathematical Physics 301 (2011), 563-581.
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Cohomological equations and invariant distributions for minimal circle
diffeomorphisms.
A. Avila, Alejandro Kocsard.
Duke Mathematical Journal 158 (2011), 501-536.
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Density of positive Lyapunov exponents for SL(2,R) cocycles.
Journal of the American Mathematical Society 24 (2011), 999-1014.
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A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies.
A. Avila, Bassam Fayad, R. Krikorian.
Geometric and Functional Analysis 21 (2011), 1001-1019.
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The full renormalization horseshoe for unimodal maps of higher degree:
exponential contraction along hybrid classes.
A. Avila, M. Lyubich.
Publications Mathématiques de l'IHÉS 114 (2011),
171-223.
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Mixing for time-changes of Heisenberg nilflows.
A. Avila, G. Forni, Corinna Ulcigrai.
Journal of Differential Geometry 89 (2011), 369-410.
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Opening gaps in the spectrum of strictly ergodic Schrödinger operators.
A. Avila, J. Bochi, D. Damanik.
Journal of the European Mathematical Society 14 (2012), 61-106.
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Nonuniform hyperbolicity, global dominated splittings and generic properties
of volume-preserving diffeomorphisms.
A. Avila, J. Bochi.
Transactions of the American Mathematical Society 364 (2012),
2883-2907.
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Exponential Mixing for the Teichmüller flow in the Space of Quadratic
Differentials.
A. Avila, Maria João Resende.
Commentarii Mathematici Helvetici 87 (2012), 589-638.
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Small eigenvalues of the Laplacian for algebraic measures in moduli space,
and mixing properties of the Teichmüller flow.
A. Avila, S. Gouëzel.
Annals of Mathematics 178 (2013), 385-442.
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SL(2,R)-invariant probability measures on the moduli spaces of
translation surfaces are regular.
A. Avila, Carlos Matheus, J.-C. Yoccoz.
Geometric and Functional Analysis 23 (2013), 1705-1729.
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Holonomy invariance: rough regularity and applications to Lyapunov exponents.
A. Avila, Jimmy Santamaria, M. Viana.
Astérisque 358 (2013), 13-74.
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On rigidity of critical circle maps.
Bulletin of the Brazilian Mathematical Society 44 (2013), 601-609.
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Singular Density of States Measure for Subshift and Quasi-Periodic
Schrödinger Operators.
A. Avila, D. Damanik, Zhenghe Zhang.
Communications in Mathematical Physics 330 (2014), 469-498.
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Complex one-frequency cocycles.
A. Avila, S. Jitomirskaya, Christian Sadel.
Journal of the European Mathematical Society 16 (2014), 1915-1935.
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On manifolds supporting distributionally uniquely ergodic diffeomorphisms.
A. Avila, B. Fayad, A. Kocsard.
Journal of Differential Geometry 99 (2015), 191-213.
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On the Kotani-Last and Schrödinger conjectures.
Journal of the American Mathematical Society 28 (2015), 579-616.
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Absolute continuity, Lyapunov exponents and rigidity I: geodesic
flows.
A. Avila, M. Viana, A. Wilkinson.
Journal of the European Mathematical Society 17 (2015), 1435-1462.
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The visits to zero of a random walk driven by an irrational rotation.
A. Avila, Dmitry Dolgopyat, Eduard Duryev, Omri Sarig.
Israel Journal of Mathematics 207 (2015), 653-717.
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Monotonic cocycles.
A. Avila, R. Krikorian.
Inventiones Mathematicae 202 (2015), 271-331.
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Global theory of one-frequency Schrödinger operators.
Acta Mathematica 215 (2015) 1-54.
This version combines the preprints
Global theory of one-frequency Schrödinger operators I: stratifed
analyticity of the Lyapunov exponent and the boundary of nonuniform
hyperbolicity,
Global theory of one-frequency Schrödinger operators II: acriticality and
finiteness of phase transitions for typical potentials.
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Weak mixing directions in non-arithmetic Veech surfaces.
A. Avila, Vincent Delecroix.
Journal of the American Mathematical Society 29 (2016), 1167-1208.
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Towers for commuting endomorphisms, and combinatorial applications.
A. Avila, Pablo Candela.
Annales de l'Institut Fourier 66 (2016), 1529-1544.
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An integrable deformation of an ellipse of small eccentricity is an
ellipse.
A. Avila, Jacopo de Simoi, Vadim Kaloshin.
Annals of Mathematics 184 (2016), 527-558.
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On the Hausdorff dimension of the Rauzy gasket.
A. Avila, Pascal Hubert, Alexandra Skripchenko.
Bulletin de la Société Mathématique de France 144 (2016), 539-568.
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Diffusion for chaotic plane sections of 3-periodic surfaces.
A. Avila, P. Hubert, A. Skripchenko.
Inventiones Mathematicae 206 (2016), 109-146.
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Diffeomorphisms with positive metric entropy.
A. Avila, Sylvain Crovisier, A. Wilkinson.
Publications Mathématiques de l'IHÉS 124 (2016),
319-347.
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Spectral Theory of Extended Harper's Model and a Question by
Erdős and Szekeres.
A. Avila, S. Jitomirskaya, Chris Marx.
Inventiones Mathematicae 210 (2017), 283-339.
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Sharp Phase transitions for the almost Mathieu operator.
A. Avila, Jiangong You, Qi Zhou.
Duke Mathematical Journal 166 (2017), 2697-2718.
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Symplectic and isometric SL(2,R)-invariant subbundles of the Hodge bundle.
A. Avila, Alex Eskin, Martin Möller.
Journal für die reine und angewandte Mathematik 732 (2017),
1-20.
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Second phase transition line.
A. Avila, S. Jitomirskaya, Q. Zhou.
Mathematische Annalen 370 (2018), 271-285.
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Zorich conjecture for hyperelliptic Rauzy-Veech groups.
A. Avila, C. Matheus, J.-C. Yoccoz.
Mathematische Annalen 370 (2018), 785-809.
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Livsic theorem for diffeomorphism cocycles.
A. Avila, A. Kocsard, Xiao-Chuan Liu.
Geometric and Functional Analysis 28 (2018), 943-964.
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Statistical properties of quadratic polynomials with a neutral fixed point.
A. Avila, Davoud Cheraghi.
Journal of the European Mathematical Society 20 (2018), 2005-2062.
Accepted for
publication
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Recurrence for the wind-tree model.
A. Avila, P. Hubert.
To appear in Annales de l'Institut Henri Poincaré - Analyse non
linéaire.
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Weak mixing properties of interval exchange transformations and translation
flows.
A. Avila, Martin Leguil.
To appear in Bulletin de la Société Mathématique
de France.
Submitted for publication
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On mixing diffeomorphisms of the disk.
A. Avila, B. Fayad, Patrice Le Calvez, Disheng Xu, Zhiyuan Zhang.
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Lebesgue measure of Feigenbaum Julia sets.
A. Avila, M. Lyubich.
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The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric
translation surfaces.
A. Avila, C. Matheus, J.-C. Yoccoz.
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Smooth Siegel disks everywhere.
A. Avila, X. Buff, A. Chéritat.
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Some monoids of Pisot matrices.
A. Avila, V. Delecroix.
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$C^1$-density of stable ergocicity.
A. Avila, S. Crovisier, A. Wilkinson.
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Stable accessibility with 2-dimensional center.
A. Avila, M. Viana.
Preprints
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Smooth Siegel disks via semicontinuity: a remark on a proof of Buff and Cheritat.
Not intended for publication.
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The absolutely continuous spectrum of the almost Mathieu operator.
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On point spectrum with critical coupling.
Not intended for publication.
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Distortion elements in $Diff^\infty(R/Z)$.
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Almost reducibility and absolute continuity I.
In preparation
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Hausdorff dimension and the quadratic family.
A. Avila, C. G. Moreira.
Expository
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Bifurcations d'applications unimodales.
C. R. Acad. Sci. Paris, Ser. I 334 (2002), 483-488. (French/English).
There is a
corrigendum
(which only affects the french version).
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Bifurcations of unimodal maps.
A. Avila, C. G. Moreira.
In ``Dynamical Systems. Part II: Topological Geometrical and Ergodic
Properties of Dynamics.''
Pubblicazioni della Classe di Scienze, Scuola Normale
Superieure, Pisa. Centro di Ricerca Matematica ``Ennio De Giorgi'':
Proceedings, pp. 1-22, 2003.
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Dynamics in the moduli space of Abelian differentials.
A. Avila, Marcelo Viana.
Portugaliae Mathematica 62 (2005), 531-547.
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Solving the Ten Martini Problem.
A. Avila, Svetlana Jitomirskaya.
Lecture Notes in Physics 690 (2006), 5-16.
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Chaoticity of the Teichmüller flow.
Clay Mathematics Proceedings 10 (2010), 321-338.
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Dynamics of renormalization operators.
In ``Proceeding of the International Congress of Mathematicians 2010.
Volume 1.'' World Scientific Publishing, pp. 154-175.
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Cocycles over partially hyperbolic maps.
A. Avila, M. Viana, A. Wilkinson.
Astérisque 358 (2013), 1-12.