4 citations · 4 across the 2 of their papers we have counts for
5 papers · 1 filter
Bifurcations of unimodal maps
Artur Avila, Carlos Gustavo Moreira
We review recent results that lead to a very precise understanding of the dynamics of typical unimodal maps from the statistical point of view. We also describe the (generalized) r…
Phase-parameter relation and sharp statistical properties for general families of unimodal maps
Artur Avila, Carlos Gustavo Moreira
We obtain estimates relating the phase space and the parameter space of analytic families of unimodal maps. Using those estimates, we show that typical analytic unimodal maps admit…
Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family
Artur Avila, Carlos Gustavo Moreira
We consider quasisymmetric reparametrizations of the parameter space of the quadratic family. We prove that the set of quadratic maps which are either regular or Collet-Eckmann wit…
Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative
Artur Avila, Carlos Gustavo Moreira
We prove that there is a residual set of families of smooth or analytic unimodal maps with quadratic critical point and negative Schwarzian derivative such that almost every non-re…
Statistical properties of unimodal maps: the quadratic family
Artur Avila, Carlos Gustavo Moreira
We prove that almost every non-regular real quadratic map is Collet-Eckmann and has polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that typ…