Blender-horseshoes in center-unstable H\'enon-like families

Abstract

A blender-horseshoe is a locally maximal transitive hyperbolic set that appears in dimension at least three carrying a distinctive geometrical property: its local stable manifold "behaves" as a manifold of topological dimension greater than the expected one (the dimension of the stable bundle). This property persists under perturbations turning this kind of dynamics an important piece in the global description of robust non-hyperbolic systems. In this paper, we consider a parameterized family of center-unstable H\'enon-like of endomorphisms in dimension three and show how blender-horseshoes naturally occur in a specific parameter range.