English

Critical points for surface maps and the Benedicks-Carleson theorem

Dynamical Systems 2010-11-19 v4

Abstract

We give an alternative proof of the Benedicks-Carleson theorem on the existence of strange attractors in H\'enon-like families in the plane. To bypass a huge inductive argument, we introduce an induction-free explicit definition of dynamically critical points. The argument is sufficiently general and in particular applies to the case of non-invertible maps as well. It naturally raises the question of an intrinsic characterization of dynamically critical points for dissipative surface maps.

Keywords

Cite

@article{arxiv.0704.1599,
  title  = {Critical points for surface maps and the Benedicks-Carleson theorem},
  author = {Hiroki Takahasi},
  journal= {arXiv preprint arXiv:0704.1599},
  year   = {2010}
}

Comments

This paper has been withdrawn by the author. 65 pages, no figure, a new section is added which deals with a model problem