A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class
Dynamical Systems
2024-11-20 v1
Abstract
We give a -perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called Markov iterated function system, a two dimensional iterated function system in which the compositions are chosen in Markovian way. Then we apply the result to the setting of three dimensional partially hyperbolic diffeomorphisms.
Keywords
Cite
@article{arxiv.2209.13245,
title = {A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class},
author = {Christian Bonatti and Katsutoshi Shinohara},
journal= {arXiv preprint arXiv:2209.13245},
year = {2024}
}