Historic and physical wandering domains for wild blender-horseshoes

Abstract

We present diffeomorphisms of wild blender-horseshoes which belong to $C^r$ $(1\le r<\infty )$ closures of two types of diffeomorphisms, one of which has a historic contracting wandering domain, and the other has a non-trivial Dirac physical measure supported by saddle periodic orbit. It is a non-trivial extension of Colli-Vargas' model [CV01] to the higher dimensional dynamics with the use of wild blender-horseshoes.

arXiv comment26 pages, 6 figures

References in corpus (6)

• Takens' last problem and existence of non-trivial wandering domains
• Historic behavior in non-hyperbolic homoclinic classes
• Topological Entropy on Points without Physical-like Behaviour
• Invariant measures for Cherry flows
• Dirac physical measures on saddle-type fixed points
• Historic wandering domains near cycles

Cited by in corpus (1)

• Takens' Last Problem and strong pluripotency