Periods of Self-Maps on S2 Via their Homology
As usual, we denote a 2-dimensional sphere by S2. We study the periods of periodic orbits of the maps f : S2 → S2 that are either continuous or C with all their periodic orbits being hyperbolic, or transversal, or holomorphic, or transversal holomorphic. For the first time, we summarize all known re...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:303182 |
| Acceso en línea: | https://ddd.uab.cat/record/303182 https://dx.doi.org/urn:doi:10.1007/s11253-024-02308-9 |
| Access Level: | acceso abierto |
| Palabra clave: | Self-maps of the 2-dimensional sphere Set of periods Periodic points Lefschetz numbers |
| Sumario: | As usual, we denote a 2-dimensional sphere by S2. We study the periods of periodic orbits of the maps f : S2 → S2 that are either continuous or C with all their periodic orbits being hyperbolic, or transversal, or holomorphic, or transversal holomorphic. For the first time, we summarize all known results on the periodic orbits of these distinct kinds of self-maps on S2 together. We note that every time when a map f : S2 → S2 increases its structure, the number of periodic orbits provided by its action on the homology increases. |
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