C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic

Let X be a connected closed manifold and f a self-map on X. We say that f is almost quasi-unipotent if every eigenvalue λ of the map f∗k (the induced map on the k-th homology group of X) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of λ as eigenvalue of...

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Autores: Llibre, Jaume|||0000-0002-9511-5999, Sirvent, Víctor F.
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:261059
Acceso en línea:https://ddd.uab.cat/record/261059
https://dx.doi.org/urn:doi:10.21136/MB.2016.6
Access Level:acceso abierto
Palabra clave:Hyperbolic periodic point
Differentiable map
Lefschetz number
Lefschetz zeta function
Quasi-unipotent map
Almost quasi-unipotent map
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spelling C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolicLlibre, Jaume|||0000-0002-9511-5999Sirvent, Víctor F.Hyperbolic periodic pointDifferentiable mapLefschetz numberLefschetz zeta functionQuasi-unipotent mapAlmost quasi-unipotent mapLet X be a connected closed manifold and f a self-map on X. We say that f is almost quasi-unipotent if every eigenvalue λ of the map f∗k (the induced map on the k-th homology group of X) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of λ as eigenvalue of all the maps f∗k with k odd is equal to the sumof the multiplicities of λ as eigenvalue of all the maps f∗k with k even. We prove that if f is C1 having finitely many periodic points all of them hyperbolic, then f is almost quasi-unipotent. 22016-01-0120162016-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/261059https://dx.doi.org/urn:doi:10.21136/MB.2016.6reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410European Commission https://doi.org/10.13039/501100000780 316338European Commission https://doi.org/10.13039/501100000780 318999open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2610592026-06-06T12:50:31Z
dc.title.none.fl_str_mv C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
title C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
spellingShingle C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
Llibre, Jaume|||0000-0002-9511-5999
Hyperbolic periodic point
Differentiable map
Lefschetz number
Lefschetz zeta function
Quasi-unipotent map
Almost quasi-unipotent map
title_short C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
title_full C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
title_fullStr C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
title_full_unstemmed C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
title_sort C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Sirvent, Víctor F.
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Sirvent, Víctor F.
author_role author
author2 Sirvent, Víctor F.
author2_role author
dc.subject.none.fl_str_mv Hyperbolic periodic point
Differentiable map
Lefschetz number
Lefschetz zeta function
Quasi-unipotent map
Almost quasi-unipotent map
topic Hyperbolic periodic point
Differentiable map
Lefschetz number
Lefschetz zeta function
Quasi-unipotent map
Almost quasi-unipotent map
description Let X be a connected closed manifold and f a self-map on X. We say that f is almost quasi-unipotent if every eigenvalue λ of the map f∗k (the induced map on the k-th homology group of X) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of λ as eigenvalue of all the maps f∗k with k odd is equal to the sumof the multiplicities of λ as eigenvalue of all the maps f∗k with k even. We prove that if f is C1 having finitely many periodic points all of them hyperbolic, then f is almost quasi-unipotent.
publishDate 2016
dc.date.none.fl_str_mv 2
2016-01-01
2016
2016-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/261059
https://dx.doi.org/urn:doi:10.21136/MB.2016.6
url https://ddd.uab.cat/record/261059
https://dx.doi.org/urn:doi:10.21136/MB.2016.6
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410
European Commission https://doi.org/10.13039/501100000780 316338
European Commission https://doi.org/10.13039/501100000780 318999
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
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://creativecommons.org/licenses/by-nc-nd/4.0/
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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repository.mail.fl_str_mv
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