A. Avila

activity

20002023

most citedThe absolutely continuous spectrum of the almost Mathieu operator

60 citations · 207 across the 32 of their papers we have counts for

collaborators

Showing 2019Show all

4 papers · 1 filter

math.DS2019

Smooth Siegel disks everywhere

Artur Avila, Xavier Buff, Arnaud Chéritat

We prove the existence of Siegel disks with smooth boundaries in most families of holomorphic maps fixing the origin. The method can also yield other types of regularity conditions…

math.DS2019

Non-differentiable irrational curves for $C^{1}$ twist map

Artur Avila, Bassam Fayad

We construct a $C^{1}$ symplectic twist map $g$ of the annulus that has an essential invariant curve $Γ$ such that $Γ$ is not differentiable and $g$ restricted to $Γ$ is minimal.

math.DS2019

Mixing for Smooth Time-Changes of General Nilflows

Artur Avila, Giovanni Forni, Davide Ravotti +1

We consider completely irrational nilflows on any nilmanifold of step at least $2$ . We show that there exists a dense set of smooth time-changes such that any time-change in this c…

math.DS2019

Symplectomorphisms with positive metric entropy

Artur Avila, Sylvain Crovisier, Amie Wilkinson

We obtain a dichotomy for $C^{1}$ -generic symplectomorphisms: either all the Lyapunov exponents of almost every point vanish, or the map is partially hyperbolic and ergodic with resp…

Smooth Siegel disks everywhere

Non-differentiable irrational curves for C1 twist map

Mixing for Smooth Time-Changes of General Nilflows

Symplectomorphisms with positive metric entropy

Non-differentiable irrational curves for $C^{1}$ twist map