Periods of Self-Maps on S2 Via their Homology
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	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.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Self-maps of the 2-dimensional sphere ; Set of periods ; Periodic points ; Lefschetz numbers
Published in:	Ukrainian Mathematical Journal, Vol. 76, Issue 1 (June 2024) , p. 76-79, ISSN 1573-9376

DOI: 10.1007/s11253-024-02308-9

Postprint 6 p, 213.2 KB

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