60 citations · 125 across the 14 of their papers we have counts for
5 papers · 2 filters
The absolutely continuous spectrum of the almost Mathieu operator
Artur Avila
We prove that the spectrum of the almost Mathieu operator is absolutely continuous if and only if the coupling is subcritical. This settles Problem 6 of Barry Simon's list of Schrö…
On the regularization of conservative maps
Artur Avila
We show that smooth maps are -dense among volume preserving maps.
Distortion elements in
Artur Avila
We consider the group of smooth diffeomorphisms of the circle. We show that any recurrent (in the sense that is not discrete) is in fact a distortion elemen…
Almost localization and almost reducibility
Artur Avila, Svetlana Jitomirskaya
We develop a quantitative version of Aubry duality and use it to obtain several sharp estimates for the dynamics of Schrödinger cocycles associated to a non-perturbatively small an…
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps
Artur Avila, Mikhail Lyubich, Weixiao Shen
We study the parameter space of unicritical polynomials . For complex parameters, we prove that for Lebesgue almost every , the map is either hyperboli…