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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Detalles Bibliográficos
Autor: Llibre, Jaume|||0000-0002-9511-5999
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
Descripción
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.