Cantor exchange systems and renormalization

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/10400.22/6656
Resumo: We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.
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spelling Cantor exchange systems and renormalizationWe prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.Academic Press Inc. Elsevier ScienceRepositório Científico do Instituto Politécnico do PortoPinto, Alberto A.Rand, David A.Ferreira, Flávio2015-10-08T14:24:07Z20072007-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/6656engPinto, A. A., Rand, D. A., & Feffeira, F. (2007). Cantor exchange systems and renormalization. Journal of Differential Equations, 243(2), 593–616. DOI: 10.1016/j.jde.2007.09.0140022-0396E-ISSN 1090-273210.1016/j.jde.2007.09.014info: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:10400.22/6656Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:27:12.941721Repositório 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 Cantor exchange systems and renormalization
title Cantor exchange systems and renormalization
spellingShingle Cantor exchange systems and renormalization
Pinto, Alberto A.
title_short Cantor exchange systems and renormalization
title_full Cantor exchange systems and renormalization
title_fullStr Cantor exchange systems and renormalization
title_full_unstemmed Cantor exchange systems and renormalization
title_sort Cantor exchange systems and renormalization
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 a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-01-01T00:00:00Z
2015-10-08T14:24:07Z
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/10400.22/6656
url http://hdl.handle.net/10400.22/6656
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Pinto, A. A., Rand, D. A., & Feffeira, F. (2007). Cantor exchange systems and renormalization. Journal of Differential Equations, 243(2), 593–616. DOI: 10.1016/j.jde.2007.09.014
0022-0396
E-ISSN 1090-2732
10.1016/j.jde.2007.09.014
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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