Blenders in centre unstable Hénon-like families: with an application to heterodimensional bifurcations

Abstract

We give an explicit family of polynomial maps called centre unstable Hénon-like maps and prove that they exhibit blenders for some parameter values. Using this family, we also prove the occurrence of blenders near certain non-transverse heterodimensional cycles under high regularity assumptions. The proof involves a renormalization scheme along heteroclinic orbits. We also investigate the connection between the blender and the original heterodimensional cycle.