A rotational hyperbolic theory for surface homeomorphisms
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918282581245952 |
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| author | Guihéneuf, Pierre-Antoine |
| author_facet | Guihéneuf, Pierre-Antoine |
| contents | We develop a rotational hyperbolic theory for surface homeomorphisms. We use the equivalence relation on ergodic measures that have nontrivial rotational behaviour defined in [arXiv:2312.06249] to define a rotational counterpart of homoclinic classes. These allows to produce a network of horseshoes representing the whole rotational behaviour f the homeomorphism. We also study the counterpart of heteroclinic connections and give 5 different characterizations of such connections.
The main technical tool is the forcing theory of Le Calvez and Tal [arXiv:1503.09127], [arXiv:1803.04557], and in particular a result of creation of periodic points that can also be seen as a statement of homotopically bounded deviations [arXiv:2511.14222].
This theoretical article is followed by a paper focused of some applications of it to the case of homeomorphisms with big rotation set [arXiv:2511.15220]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A rotational hyperbolic theory for surface homeomorphisms Guihéneuf, Pierre-Antoine Dynamical Systems 37E45, 37E30, 37D20 We develop a rotational hyperbolic theory for surface homeomorphisms. We use the equivalence relation on ergodic measures that have nontrivial rotational behaviour defined in [arXiv:2312.06249] to define a rotational counterpart of homoclinic classes. These allows to produce a network of horseshoes representing the whole rotational behaviour f the homeomorphism. We also study the counterpart of heteroclinic connections and give 5 different characterizations of such connections. The main technical tool is the forcing theory of Le Calvez and Tal [arXiv:1503.09127], [arXiv:1803.04557], and in particular a result of creation of periodic points that can also be seen as a statement of homotopically bounded deviations [arXiv:2511.14222]. This theoretical article is followed by a paper focused of some applications of it to the case of homeomorphisms with big rotation set [arXiv:2511.15220]. |
| title | A rotational hyperbolic theory for surface homeomorphisms |
| topic | Dynamical Systems 37E45, 37E30, 37D20 |
| url | https://arxiv.org/abs/2511.14232 |