Critical points for surface maps and the Benedicks-Carleson theorem

Hiroki Takahasi

Keywords: Henon-like maps | strange attractors

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

Anexos:

• basinproblem.pdf