English

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