Abstract

We present a (new) proof of the existence of a non uniformly hyperbolic attractor for a positive set of parameters $a$ in the family of endomorphisms: [(x,y)mapsto (x2+a+2y,0)+B(x,y)] Where $B$ is fixed a $C2$ small function. For $B=(0,x)$ we get the Henon map. The proof uses the formalism of Yoccoz puzzle and analytical ideas of Benedicks-Carleson. The proof uses formalisms from analysis, geometry, algebra and probability.