Critical points for surface maps and the Benedicks-Carleson theorem

Details Critical points for surface maps and the Benedicks-Carleson theorem Critical points for surface maps and the Benedicks-Carleson theorem

2007-04-12

arxiv.org/abs/0704.1599v4

Mathematics

Dynamical Systems

This paper has been withdrawn by the author. 65 pages, no figure, a new section is added which deals with a model problem

Scientific paper

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.

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