Topological entropy of continuous self–maps on a graph

Let G be a graph and f be a continuous self–map on G. We provide sufficient conditions based on the Lefschetz zeta function in order that f has positive topological entropy. Moreover, for the particular graphs: p–flower graph, n-lips graph and (p+r1L1+:::+rsLs)–graph we are able to go further and st...

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Detalles Bibliográficos
Autores: García Guirao, Juan Luis, Llibre Saló, Jaume, Gao, Wei
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad Politécnica de Cartagena(UPCT)
Repositorio:Repositorio Digital UPCT
OAI Identifier:oai:repositorio.upct.es:10317/8502
Acceso en línea:http://hdl.handle.net/10317/8502
https://link.springer.com/article/10.1007%2Fs40314-019-0969-3
Access Level:acceso abierto
Palabra clave:Topological graph
Discrete dynamical systems
Lefschetz numbers
Lefschetz zeta function
Periodic point
Period
Topological entropy
Matemática Aplicada
12 Matemáticas
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spelling Topological entropy of continuous self–maps on a graphGarcía Guirao, Juan LuisLlibre Saló, JaumeGao, WeiTopological graphDiscrete dynamical systemsLefschetz numbersLefschetz zeta functionPeriodic pointPeriodTopological entropyMatemática Aplicada12 MatemáticasLet G be a graph and f be a continuous self–map on G. We provide sufficient conditions based on the Lefschetz zeta function in order that f has positive topological entropy. Moreover, for the particular graphs: p–flower graph, n-lips graph and (p+r1L1+:::+rsLs)–graph we are able to go further and state more precise conditions for having positive topological entropy.The second author is partially supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación grants MTM-2016-77278-P (FEDER) and MDM-2014-0445, the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911.Springer Science and Business MediaMinisterio de Economía, Industria y CompetitividadAgència de Gestiö d'Ajuts Universitaris i de RecercaEuropean Research Council202020202019info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10317/8502https://link.springer.com/article/10.1007%2Fs40314-019-0969-3reponame:Repositorio Digital UPCTinstname:Universidad Politécnica de Cartagena(UPCT)Ingléshttps://link.springer.com/article/10.1007%2Fs40314-019-0969-3MTM-2016-77278-PMDM-2014-04452017SGR1617MSCA-RISE-2017-777911Atribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:repositorio.upct.es:10317/85022026-05-15T06:39:02Z
dc.title.none.fl_str_mv Topological entropy of continuous self–maps on a graph
title Topological entropy of continuous self–maps on a graph
spellingShingle Topological entropy of continuous self–maps on a graph
García Guirao, Juan Luis
Topological graph
Discrete dynamical systems
Lefschetz numbers
Lefschetz zeta function
Periodic point
Period
Topological entropy
Matemática Aplicada
12 Matemáticas
title_short Topological entropy of continuous self–maps on a graph
title_full Topological entropy of continuous self–maps on a graph
title_fullStr Topological entropy of continuous self–maps on a graph
title_full_unstemmed Topological entropy of continuous self–maps on a graph
title_sort Topological entropy of continuous self–maps on a graph
dc.creator.none.fl_str_mv García Guirao, Juan Luis
Llibre Saló, Jaume
Gao, Wei
author García Guirao, Juan Luis
author_facet García Guirao, Juan Luis
Llibre Saló, Jaume
Gao, Wei
author_role author
author2 Llibre Saló, Jaume
Gao, Wei
author2_role author
author
dc.contributor.none.fl_str_mv Ministerio de Economía, Industria y Competitividad
Agència de Gestiö d'Ajuts Universitaris i de Recerca
European Research Council
dc.subject.none.fl_str_mv Topological graph
Discrete dynamical systems
Lefschetz numbers
Lefschetz zeta function
Periodic point
Period
Topological entropy
Matemática Aplicada
12 Matemáticas
topic Topological graph
Discrete dynamical systems
Lefschetz numbers
Lefschetz zeta function
Periodic point
Period
Topological entropy
Matemática Aplicada
12 Matemáticas
description Let G be a graph and f be a continuous self–map on G. We provide sufficient conditions based on the Lefschetz zeta function in order that f has positive topological entropy. Moreover, for the particular graphs: p–flower graph, n-lips graph and (p+r1L1+:::+rsLs)–graph we are able to go further and state more precise conditions for having positive topological entropy.
publishDate 2019
dc.date.none.fl_str_mv 2019
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10317/8502
https://link.springer.com/article/10.1007%2Fs40314-019-0969-3
url http://hdl.handle.net/10317/8502
https://link.springer.com/article/10.1007%2Fs40314-019-0969-3
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://link.springer.com/article/10.1007%2Fs40314-019-0969-3
MTM-2016-77278-P
MDM-2014-0445
2017SGR1617
MSCA-RISE-2017-777911
dc.rights.none.fl_str_mv Atribución-NoComercial-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Science and Business Media
publisher.none.fl_str_mv Springer Science and Business Media
dc.source.none.fl_str_mv reponame:Repositorio Digital UPCT
instname:Universidad Politécnica de Cartagena(UPCT)
instname_str Universidad Politécnica de Cartagena(UPCT)
reponame_str Repositorio Digital UPCT
collection Repositorio Digital UPCT
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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