Blenders for a non-normally Henon-like family

Abstract

A blender is an indispensable concept presented by Bonatti and Diaz [3] to study high-dimensional $C^1$-robust transitive dynamics around heterodimensional cycles. In this paper, we present a certain Henon-like family of real quadratic diffeomorphisms on $\mathbb{R}^3$, which exhibits an phase transition from non-normal horseshoes to blenders. It can be observable from a rapidly jump of topological dimension for some projected stable segments in some characteristic region of $\mathbb{R}^3$.