Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

Detalhes bibliográficos
Autor(a) principal: Pinto, Alberto A.
Data de Publicação: 2007
Outros Autores: Rand, David A., Ferreira, Flávio
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/6654
Resumo: We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.
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spelling Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamicsWe prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.Academic Press Inc. Elsevier ScienceRepositório Científico do Instituto Politécnico do PortoPinto, Alberto A.Rand, David A.Ferreira, Flávio2015-10-08T13:24:11Z20072007-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/6654engPinto, A. A., Rand, D. A., & Ferreira, E. (2007). Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics. Journal of Differential Equations, 243(2), 168–178. DOI: 10.1016/j.jde.2007.02.01310.1016/j.jde.2007.02.013info: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:RCAAP2023-03-13T12:47:03Zoai:recipp.ipp.pt:10400.22/6654Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:27:13.106253Repositório 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 Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
title Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
spellingShingle Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
Pinto, Alberto A.
title_short Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
title_full Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
title_fullStr Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
title_full_unstemmed Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
title_sort Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
author Pinto, Alberto A.
author_facet Pinto, Alberto A.
Rand, David A.
Ferreira, Flávio
author_role author
author2 Rand, David A.
Ferreira, Flávio
author2_role author
author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico do Porto
dc.contributor.author.fl_str_mv Pinto, Alberto A.
Rand, David A.
Ferreira, Flávio
description We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-01-01T00:00:00Z
2015-10-08T13:24:11Z
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/10400.22/6654
url http://hdl.handle.net/10400.22/6654
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Pinto, A. A., Rand, D. A., & Ferreira, E. (2007). Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics. Journal of Differential Equations, 243(2), 168–178. DOI: 10.1016/j.jde.2007.02.013
10.1016/j.jde.2007.02.013
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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)
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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
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