93 citations · 950 across the 70 of their papers we have counts for
83 papers
KAM, Lyapunov exponents, and the Spectral Dichotomy for typical one-frequency Schrodinger operators
Artur Avila
We show that a one-frequency analytic SL(2,R) cocycle with Diophantine rotation vector is analytically linearizable if and only if the Lyapunov exponent is zero through a complex n…
Dry Ten Martini Problem in the non-critical case
Artur Avila, Jiangong You, Qi Zhou
We solve the Dry Ten Martini Problem in the non-critical case, i.e., all possible spectral gaps are open for almost Mathieu operators with .
Continuity of the Lyapunov exponents of random matrix products
Artur Avila, Alex Eskin, Marcelo Viana
We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally,…
The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials
Artur Avila, David Damanik, Anton Gorodetski
We consider Schrödinger operators in whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the…
On the abominable properties of the almost Mathieu operator with well approximated frequencies
Artur Avila, Yoram Last, Mira Shamis +1
We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensi…
Quantitative weak mixing for interval exchange transformations
Artur Avila, Giovanni Forni, Pedram Safaee
We establish a dichotomy for the rate of the decay of the Cesàro averages of correlations of sufficiently regular functions for typical interval exchange transformations (IET) whic…