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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2023

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

Résumé

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/heteroclinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called a Markov iterated function system, a two-dimensional iterated function system in which the compositions are chosen in a Markovian way. Then we apply the result to the setting of three-dimensional partially hyperbolic diffeomorphisms.

Dates et versions

hal-04362255 , version 1 (22-12-2023)

Identifiants

Citer

C. Bonatti, Katsutoshi Shinohara. A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class. Ergodic Theory and Dynamical Systems, 2023, pp.1-63. ⟨10.1017/etds.2023.76⟩. ⟨hal-04362255⟩
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