A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913580568281088 |
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| author | Bonatti, Christian Shinohara, Katsutoshi |
| author_facet | Bonatti, Christian Shinohara, Katsutoshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13245 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class Bonatti, Christian Shinohara, Katsutoshi Dynamical Systems 37B25, 37D30, 37G35 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. |
| title | A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class |
| topic | Dynamical Systems 37B25, 37D30, 37G35 |
| url | https://arxiv.org/abs/2209.13245 |