93 citations · 950 across the 70 of their papers we have counts for
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Generic singular continuous spectrum for ergodic Schrödinger operators
Artur Avila, David Damanik
We consider Schrödinger operators with ergodic potential , , , where is a non-periodic homeomorphism. We show that for generic $f \in…
Hausdorff dimension and conformal measures of Feigenbaum Julia sets
Artur Avila, Mikhail Lyubich
We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon'', there exist many Feigenbaum Julia s…
Examples of Feigenbaum Julia sets with small Hausdorff dimension
Artur Avila, Mikhail Lyubich
We give examples of infinitely renormalizable quadratic polynomials $F_c: z\maps to z^2+c$ with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrar y close…
Weak mixing for interval exchange transformations and translation flows
Artur Avila, Giovanni Forni
We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of ge…