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

Abstract

We give an explicit family of polynomial maps called center unstable Hénon-like maps and prove that they exhibits blenders for some parametervalues. 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.

References in corpus (1)

• Heterodimensional tangencies on cycles leading to strange attractors

Cited by in corpus (3)

• Piecewise-linear maps with heterogeneous chaos
• Indestructible dynamics of torus maps
• Hénon-like families and blender-horseshoes at non-transverse heterodimensional cycles