Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

Detalhes bibliográficos
Autor(a) principal: Horita, Vanderlei [UNESP]
Data de Publicação: 2005
Outros Autores: Viana, Marcelo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://aimsciences.org/journals/pdfs.jsp?paperID=1107&mode=abstract
http://dx.doi.org/10.3934/dcds.2005.13.1125
http://hdl.handle.net/11449/68499
Resumo: We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.
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spelling Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphismsDimension theoryNon-uniform hyperbolicityRepellerWe study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.Departamento de Matemática IBILCE/UNESP, Rua Cristovao Colombo, 2265, 15055-S. J. Rio Preto, SPIMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJDepartamento de Matemática IBILCE/UNESP, Rua Cristovao Colombo, 2265, 15055-S. J. Rio Preto, SPUniversidade Estadual Paulista (Unesp)IMPAHorita, Vanderlei [UNESP]Viana, Marcelo2014-05-27T11:21:40Z2014-05-27T11:21:40Z2005-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1125-1152application/pdfhttp://aimsciences.org/journals/pdfs.jsp?paperID=1107&mode=abstracthttp://dx.doi.org/10.3934/dcds.2005.13.1125Discrete and Continuous Dynamical Systems, v. 13, n. 5, p. 1125-1152, 2005.1078-0947http://hdl.handle.net/11449/6849910.3934/dcds.2005.13.1125WOS:0002305322000022-s2.0-284444720202-s2.0-28444472020.pdf0000-0002-9304-0655Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengDiscrete and Continuous Dynamical Systems0.9761,592info:eu-repo/semantics/openAccess2023-12-08T06:17:25Zoai:repositorio.unesp.br:11449/68499Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:45:05.060962Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms
title Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms
spellingShingle Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms
Horita, Vanderlei [UNESP]
Dimension theory
Non-uniform hyperbolicity
Repeller
title_short Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms
title_full Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms
title_fullStr Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms
title_full_unstemmed Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms
title_sort Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms
author Horita, Vanderlei [UNESP]
author_facet Horita, Vanderlei [UNESP]
Viana, Marcelo
author_role author
author2 Viana, Marcelo
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
IMPA
dc.contributor.author.fl_str_mv Horita, Vanderlei [UNESP]
Viana, Marcelo
dc.subject.por.fl_str_mv Dimension theory
Non-uniform hyperbolicity
Repeller
topic Dimension theory
Non-uniform hyperbolicity
Repeller
description We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.
publishDate 2005
dc.date.none.fl_str_mv 2005-12-01
2014-05-27T11:21:40Z
2014-05-27T11:21:40Z
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://aimsciences.org/journals/pdfs.jsp?paperID=1107&mode=abstract
http://dx.doi.org/10.3934/dcds.2005.13.1125
Discrete and Continuous Dynamical Systems, v. 13, n. 5, p. 1125-1152, 2005.
1078-0947
http://hdl.handle.net/11449/68499
10.3934/dcds.2005.13.1125
WOS:000230532200002
2-s2.0-28444472020
2-s2.0-28444472020.pdf
0000-0002-9304-0655
url http://aimsciences.org/journals/pdfs.jsp?paperID=1107&mode=abstract
http://dx.doi.org/10.3934/dcds.2005.13.1125
http://hdl.handle.net/11449/68499
identifier_str_mv Discrete and Continuous Dynamical Systems, v. 13, n. 5, p. 1125-1152, 2005.
1078-0947
10.3934/dcds.2005.13.1125
WOS:000230532200002
2-s2.0-28444472020
2-s2.0-28444472020.pdf
0000-0002-9304-0655
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems
0.976
1,592
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1125-1152
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129113462931456

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