In this talk, we will discuss the dynamics of a family of toy models introduced by Benedicks-Carleson (which are simplified versions of Henon attractors). In particular, we show two results: firstly, we exhibit a C^2 open set of toy models whose limit set is not hyperbolic (Newhouse phenomena); secondly, we prove that Axiom A is a C^1 dense property among the toy models. Finally, if the time permits, we pretend to discuss how a sightly modification of this argument provides strong support for a positive answer to Smale's conjecture about C^1 density of Axiom A surface diffeomorphisms. This is a joint work with C. G. Moreira and E. Pujals.