Historic and physical wandering domains for wild blender-horseshoes

Abstract

We present diffeomorphisms of wild blender-horseshoes which belong to $C^r$ $(1\leq r<\infty)$ 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.

Figures (7)

• Figure 1.1:
• Figure 1.2:
• Figure 1.3:
• Figure 2.1:
• Figure 2.2:

Theorems & Definitions (40)

• Theorem A
• Remark 1.1
• Remark 1.2: Asymmetricity
• Lemma 1.3
• Remark 1.4: Generality of configuration
• Theorem A$\!^{\prime}$
• Lemma 2.1
• Remark 2.2
• proof : Proof of Lemma \ref{['l_zeta']}
• Proposition 2.3