Critical points for surface maps and the Benedicks-Carleson theorem

Hiroki Takahasi

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arXiv · 0704.1599

Critical points for surface maps and the Benedicks-Carleson theorem

Hiroki Takahasi

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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.

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Hiroki Takahasi. 2010-11-18. Critical points for surface maps and the Benedicks-Carleson theorem. https://arxiv.org/abs/0704.1599

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