English

A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class

Dynamical Systems 2024-11-20 v1

Abstract

We give a C1C^1-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}
}
R2 v1 2026-06-28T02:10:47.507Z