Non-trivial wandering domains for heterodimensional cycles
Dynamical Systems
2017-07-25 v3
Abstract
We present a sufficient condition for three-dimensional diffeomorphisms having heterodimensional cycles to be approximated arbitrarily well by diffeomorphisms with non-trivial contracting wandering domains via several perturbations. The key idea is to show that diffeomorphisms with heterodimensional cycles associated with saddle points with non-real eigenvalues can be approximated by diffeomorphisms with generalized homoclinic tangencies presented by Tatjer. The generalized homoclinic tangency is an organizing center including a Bogdanov-Takens bifurcation, by which one can obtain non-trivial contracting wandering domains together with a Denjoy-like construction.
Keywords
Cite
@article{arxiv.1610.02734,
title = {Non-trivial wandering domains for heterodimensional cycles},
author = {Shin Kiriki and Yushi Nakano and Teruhiko Soma},
journal= {arXiv preprint arXiv:1610.02734},
year = {2017}
}