Artur Avila

most citedA generic

C^{1}

map has no absolutely continuous invariant probability measure

51 citations · 59 across the 2 of their papers we have counts for

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math.DS2006★ 51 cited

A generic $C^{1}$ map has no absolutely continuous invariant probability measure

Artur Avila, Jairo Bochi

Let $M$ be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension $d \geq 1$ . We consider the set of $C^{1}$ maps $f : M \to M$ which have no absolutely con…

math.DS2003★ 8 cited

Statistical properties of unimodal maps: physical measures, periodic orbits and pathological laminations

Artur Avila, Carlos Gustavo Moreira

In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating…

A generic C1 map has no absolutely continuous invariant probability measure

Statistical properties of unimodal maps: physical measures, periodic orbits and pathological laminations

A generic $C^{1}$ map has no absolutely continuous invariant probability measure