Blenders for a non-normally Hénon-like family.

Abstract

The aim of this work is to study the existence of blender structure in a three-dimensional family of diffeomorphisms derived from the canonical Henon family in dimension two by multiply it by a convenient affine function in the z-direction. As in [1] we shall call the topological conjugacy class of this family for Non-normally Henon-like family. A blender is an important concept in Dynamic from the geometric point of view. The first time that the subject appears was in [2] where the authors define and use blender structure to prove the existence of some kind of robust transitive dieomeorphism far from hyperbolicity. The most deep consequence of the blender structure is that one can have one dimensional submanifold of the ambient space which behaves as two dimensional submanifold. Another fact about blenders is that one can construct affine blender as we will show in this work.