Preprint A520/2007
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.