Cantor exchange systems and renormalization
Autor(a) principal: | |
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Data de Publicação: | 2007 |
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/10400.22/6656 |
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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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) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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