Spectral invariants of periodic nonautonomous discrete dynamical systems
Autor(a) principal: | |
---|---|
Data de Publicação: | 2015 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.21/6004 |
Resumo: | For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems. |
id |
RCAP_6e6e3b54618c38670ec66b3581b88f37 |
---|---|
oai_identifier_str |
oai:repositorio.ipl.pt:10400.21/6004 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Spectral invariants of periodic nonautonomous discrete dynamical systemsNonautonomous discrete dynamical systemsInterval mapsZeta functionsSpectral invariantsTopological entropyFor an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.ACADEMIC PRESS INC ELSEVIER SCIENCERCIPLAlves, João FerreiraMálek, MichalSilva, Luís2016-04-15T16:28:19Z2015-10-012015-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/6004engALVES, João Ferreira; MÁLEK, Michal; SILVA, Luís - Spectral invariants of periodic nonautonomous discrete dynamical systems. Journal of Mathematical Analysis and Applications. ISSN. 0022-247X. Vol. 430, N.º 1 (2015), pp. 85-97.0022-247X10.1016/j.jmaa.2015.04.059metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T09:50:14Zoai:repositorio.ipl.pt:10400.21/6004Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:15:13.141529Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Spectral invariants of periodic nonautonomous discrete dynamical systems |
title |
Spectral invariants of periodic nonautonomous discrete dynamical systems |
spellingShingle |
Spectral invariants of periodic nonautonomous discrete dynamical systems Alves, João Ferreira Nonautonomous discrete dynamical systems Interval maps Zeta functions Spectral invariants Topological entropy |
title_short |
Spectral invariants of periodic nonautonomous discrete dynamical systems |
title_full |
Spectral invariants of periodic nonautonomous discrete dynamical systems |
title_fullStr |
Spectral invariants of periodic nonautonomous discrete dynamical systems |
title_full_unstemmed |
Spectral invariants of periodic nonautonomous discrete dynamical systems |
title_sort |
Spectral invariants of periodic nonautonomous discrete dynamical systems |
author |
Alves, João Ferreira |
author_facet |
Alves, João Ferreira Málek, Michal Silva, Luís |
author_role |
author |
author2 |
Málek, Michal Silva, Luís |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
RCIPL |
dc.contributor.author.fl_str_mv |
Alves, João Ferreira Málek, Michal Silva, Luís |
dc.subject.por.fl_str_mv |
Nonautonomous discrete dynamical systems Interval maps Zeta functions Spectral invariants Topological entropy |
topic |
Nonautonomous discrete dynamical systems Interval maps Zeta functions Spectral invariants Topological entropy |
description |
For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-10-01 2015-10-01T00:00:00Z 2016-04-15T16:28:19Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.21/6004 |
url |
http://hdl.handle.net/10400.21/6004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
ALVES, João Ferreira; MÁLEK, Michal; SILVA, Luís - Spectral invariants of periodic nonautonomous discrete dynamical systems. Journal of Mathematical Analysis and Applications. ISSN. 0022-247X. Vol. 430, N.º 1 (2015), pp. 85-97. 0022-247X 10.1016/j.jmaa.2015.04.059 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
ACADEMIC PRESS INC ELSEVIER SCIENCE |
publisher.none.fl_str_mv |
ACADEMIC PRESS INC ELSEVIER SCIENCE |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799133409828667392 |