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Avila, Artur

  1. The absolutely continuous spectrum of the almost Mathieu operator
    2008/10/16 by Artur Avila, Avila, Artur · 11 citations
    Mathematics · #Spectral Theory in Mathematical Physics #Holomorphic and Operator Theory #Algebraic and Geometric Analysis
  2. Almost reducibility and absolute continuity I
    2010/06/03 by Artur Avila, Avila, Artur · 9 citations
    Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics
  3. Almost localization and almost reducibility
    2008/05/12 by Artur Avila, Avila, Artur, Svetlana Jitomirskaya +1 · 4 citations
    Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
  4. An integrable deformation of an ellipse of small eccentricity is an ellipse
    2014/12/09 by Avila, Artur, De Simoi, Jacopo, Kaloshin, Vadim · 5 citations
    #Dynamical Systems (math.DS) #FOS: Mathematics
  5. On the abominable properties of the almost Mathieu operator with well approximated frequencies
    2021/10/15 by Artur Avila, Avila, Artur, Yoram Last +5 · 5 citations
    Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Quantum Mechanics and Non-Hermitian Physics
  6. Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
    2005/08/25 by Avila, Artur, Viana, Marcelo · 2 citations
    #Dynamical Systems (math.DS) #FOS: Mathematics
  7. Simplicity of Lyapunov spectra: a sufficient criterion
    2006/07/28 by Avila, Artur, Viana, Marcelo · 2 citations
    #Dynamical Systems (math.DS) #FOS: Mathematics
  8. Mixing for Time-Changes of Heisenberg Nilflows
    2010/03/24 by Artur Avila, Giovanni Forni, Avila, Artur +3 · 2 citations
    Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #advanced mathematical theories
  9. Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows
    2011/10/11 by Avila, Artur, Viana, Marcelo, Wilkinson, Amie · 2 citations
    #37C40 #37C85 #Dynamical Systems (math.DS) #FOS: Mathematics
  10. Mixing for Smooth Time-Changes of General Nilflows
    2019/05/28 by Avila, Artur, Forni, Giovanni, Ravotti, Davide +1 · 3 citations
    #Dynamical Systems (math.DS) #FOS: Mathematics
  11. Distortion elements in Diff^∞(R/Z)
    2008/08/18 by Artur Avila, Avila, Artur · 2 citations
    Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Analysis and Transform Methods #Numerical methods in engineering
  12. Non-differentiable irrational curves for C1 twist map
    2019/09/30 by Avila, Artur, Fayad, Bassam · 2 citations
    #Dynamical Systems (math.DS) #FOS: Mathematics
  13. Continuity of the Lyapunov exponents of random matrix products
    2023/05/10 by Artur Avila, Avila, Artur, Alex Eskin +3 · 3 citations
    Mathematics · Computer Science · #Mathematical Dynamics and Fractals #advanced mathematical theories #Topological and Geometric Data Analysis
  14. Weak mixing for interval exchange transformations and translation flows
    2004/06/16 by Artur Avila, Avila, Artur, Giovanni Forni +1 · 1 citation
    Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
  15. Smoothness of solenoidal attractors
    2005/03/08 by Artur Avila, Avila, Artur, Sebastien Gouezel +4 · 1 citation
    Mathematics · Physics and Astronomy · #37A25 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37A25 #msc:37D30
  16. Exponential mixing for the Teichmuller flow
    2005/11/24 by Avila, Artur, Gouezel, Sebastien, Yoccoz, Jean-Christophe · 1 citation
    #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)
  17. On the regularization of conservative maps
    2008/10/08 by Artur Avila, Avila, Artur · 1 citation
    Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Mathematical Dynamics and Fractals
  18. Exponential Mixing for the Teichmuller flow in the Space of Quadratic Differentials
    2009/08/07 by Avila, Artur, Resende, Maria Joao · 1 citation
    #37A25 #Dynamical Systems (math.DS) #FOS: Mathematics
  19. Nonuniform Hyperbolicity, Global Dominated Splittings and Generic\n Properties of Volume-Preserving Diffeomorphisms
    2009/12/14 by Artur Avila, Jairo Bochi, Avila, Artur +1 · 1 citation
    Mathematics · #Mathematical Dynamics and Fractals
  20. On the Kotani-Last and Schrodinger conjectures
    2012/10/23 by Avila, Artur · 1 citation
    #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
  21. Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative
    2001/05/27 by Artur Avila, Carlos Gustavo Moreira, Avila, Artur +1 · 1 citation
    Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #math.DS
  22. Livsic theorem for diffeomorphism cocycles
    2017/11/06 by Artur Avila, Alejandro Kocsard, Avila, Artur +3 · 1 citation
    Mathematics · Physics and Astronomy · #37H05 #37H15 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
  23. Schrödinger Operators With Potentials Generated by Hyperbolic Transformations: I. Positivity of the Lyapunov Exponent
    2020/11/19 by Avila, Artur, Damanik, David, Zhang, Zhenghe · 1 citation
    #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
  24. Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization
    2024/01/31 by Avila, Artur, Damanik, David, Zhang, Zhenghe · 1 citation
    #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
  25. The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials
    2022/11/03 by Artur Avila, David Damanik, Avila, Artur +3 · 1 citation
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
  26. Dry Ten Martini Problem in the non-critical case
    2023/06/28 by Avila, Artur, You, Jiangong, Zhou, Qi · 1 citation
    #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
  27. Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow
    2010/11/24 by Artur Avila, Avila, Artur, Sébastien Gouëzel +1 · 1 citation
    Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems