Critical points for surface maps and the Benedicks-Carleson theorem

Abstract

We give an alternative proof of the Benedicks-Carleson theorem on the existence of strange attractors in Hénon-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.

This paper has been withdrawn by the author. 65 pages, no figure, a new section is added which deals with a model problem