Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative
Dynamical Systems
2007-05-23 v3
Abstract
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-regular parameter is Collet-Eckmann with subexponential recurrence of the critical orbit. Those conditions lead to a detailed and robust statistical description of the dynamics. This proves the Palis conjecture in this setting.
Keywords
Cite
@article{arxiv.math/0105221,
title = {Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative},
author = {Artur Avila and Carlos Gustavo Moreira},
journal= {arXiv preprint arXiv:math/0105221},
year = {2007}
}
Comments
33 pages, no figures, third version, to appear in Ast\'erisque