Historic wandering domains near cycles

Abstract

We explain how to obtain non-trivial historic contractive wandering domains for a dense set of diffeomorphisms in certain type of $C^r$-Newhouse domains of homoclinic tangencies in dimension $d\ge 3$ and $r\ge 1$. In particular, this gives for the first time a contribution to Takens' last problem in the $C^1$ topology and in dimension $d>2$. We show how these Newhouse domains can be obtained arbitrarily close to diffeomorphisms exhibiting heterodimensional cycles (in dimension $d=3$) or non-transverse equidimensional cycles (in any dimension $d\ge 3$) associated with periodic points with non-real complex leading multipliers.

References in corpus (7)

• Takens' last problem and existence of non-trivial wandering domains
• Stabilization of heterodimensional cycles
• Historic behavior in non-hyperbolic homoclinic classes
• Robust tangencies of large codimension
• Topological Entropy and Diffeomorphisms of Surfaces with Wandering Domains
• Non-trivial wandering domains for heterodimensional cycles
• Berger domains and Kolmogorov typicality of infinitely many invariant circles

Cited by in corpus (3)

• Abundance of observable Lyapunov irregular sets
• Historic and physical wandering domains for wild blender-horseshoes
• Takens' Last Problem and strong pluripotency