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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Author: Llibre, Jaume|||0000-0002-9511-5999
Format: article
Publication Date:2024
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:303182
Online Access:https://ddd.uab.cat/record/303182
https://dx.doi.org/urn:doi:10.1007/s11253-024-02308-9
Access Level:Open access
Keyword:Self-maps of the 2-dimensional sphere
Set of periods
Periodic points
Lefschetz numbers
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spelling Periods of Self-Maps on S2 Via their HomologyLlibre, Jaume|||0000-0002-9511-5999Self-maps of the 2-dimensional sphereSet of periodsPeriodic pointsLefschetz numbersAs 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. 22024-01-0120242024-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/303182https://dx.doi.org/urn:doi:10.1007/s11253-024-02308-9reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00European Commission https://doi.org/10.13039/501100000780 777911Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2021/SGR-00113open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:3031822026-06-06T12:50:31Z
dc.title.none.fl_str_mv Periods of Self-Maps on S2 Via their Homology
title Periods of Self-Maps on S2 Via their Homology
spellingShingle Periods of Self-Maps on S2 Via their Homology
Llibre, Jaume|||0000-0002-9511-5999
Self-maps of the 2-dimensional sphere
Set of periods
Periodic points
Lefschetz numbers
title_short Periods of Self-Maps on S2 Via their Homology
title_full Periods of Self-Maps on S2 Via their Homology
title_fullStr Periods of Self-Maps on S2 Via their Homology
title_full_unstemmed Periods of Self-Maps on S2 Via their Homology
title_sort Periods of Self-Maps on S2 Via their Homology
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
author_role author
dc.subject.none.fl_str_mv Self-maps of the 2-dimensional sphere
Set of periods
Periodic points
Lefschetz numbers
topic Self-maps of the 2-dimensional sphere
Set of periods
Periodic points
Lefschetz numbers
description 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.
publishDate 2024
dc.date.none.fl_str_mv 2
2024-01-01
2024
2024-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/303182
https://dx.doi.org/urn:doi:10.1007/s11253-024-02308-9
url https://ddd.uab.cat/record/303182
https://dx.doi.org/urn:doi:10.1007/s11253-024-02308-9
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00
European Commission https://doi.org/10.13039/501100000780 777911
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2021/SGR-00113
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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