Conditions implying annular chaos
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908420159832064 |
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| author | Passeggi, Alejandro Tal, Fabio Armando |
| author_facet | Passeggi, Alejandro Tal, Fabio Armando |
| contents | This work investigates topological chaos for homeomorphisms of the open annulus, introducing a new set of sufficient conditions based on points with distinct rotation numbers and their topological relation to invariant continua. These conditions allow us to formulate classic methods for verifying annular chaos in a finitely verifiable version supported on basic properties of the map. The results pave the way for simple computer-assisted proofs of chaos in a wide range of annular maps, including many well known examples, and we present these proofs for some analytic families, demonstrating the effectiveness of the method. On the theoretical side, one of the consequences of the established conditions permits the proof of a folkloric conjecture about the relation between topological entropy and rotation sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02963 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conditions implying annular chaos Passeggi, Alejandro Tal, Fabio Armando Dynamical Systems 37E30 This work investigates topological chaos for homeomorphisms of the open annulus, introducing a new set of sufficient conditions based on points with distinct rotation numbers and their topological relation to invariant continua. These conditions allow us to formulate classic methods for verifying annular chaos in a finitely verifiable version supported on basic properties of the map. The results pave the way for simple computer-assisted proofs of chaos in a wide range of annular maps, including many well known examples, and we present these proofs for some analytic families, demonstrating the effectiveness of the method. On the theoretical side, one of the consequences of the established conditions permits the proof of a folkloric conjecture about the relation between topological entropy and rotation sets. |
| title | Conditions implying annular chaos |
| topic | Dynamical Systems 37E30 |
| url | https://arxiv.org/abs/2305.02963 |