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arXiv · 2209.13245

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

Christian Bonatti·Katsutoshi Shinohara
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Abstract

We give a $C^1$-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.

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Christian Bonatti, Katsutoshi Shinohara. 2022-09-27. A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class. https://doi.org/10.1017/etds.2023.76

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