Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models
We consider a family of planar systems introduced in 1991 by Benedicks and Carleson as a toy model for the dynamics of the so-called Hénon maps. We show that Smale’s Axiom A property is -dense among the systems in this family, despite the existence of -open subsets (closely related to the so-called Newhouse phenomena) where Smale’s Axiom A is violated. In particular, this provides some evidence towards Smale’s conjecture that Axiom A is a -dense property among surface diffeomorphisms. The basic...