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 (2)

• Robust tangencies of large codimension
• 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