Arc exchange systems and renormalization
Autor(a) principal: | |
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Data de Publicação: | 2010 |
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/10400.22/6657 |
Resumo: | We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system. |
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Arc exchange systems and renormalizationHyperbolic dynamicsRenormalizationMarkov mapsMinimal setsWe exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.Taylor & FrancisRepositório Científico do Instituto Politécnico do PortoPinto, Alberto A.Rand, David A.Ferreira, Flávio2015-10-08T14:34:48Z20102010-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/10400.22/6657engA.A. Pinto , D.A. Rand & F. Ferreira (2010) Arc exchange systems and renormalization, Journal of Difference Equations and Applications, 16:4, 347-371, DOI: 10.1080/102361908024220591023-619810.1080/10236190802422059info: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:10400.22/6657Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:27:13.058610Repositório 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 |
Arc exchange systems and renormalization |
title |
Arc exchange systems and renormalization |
spellingShingle |
Arc exchange systems and renormalization Pinto, Alberto A. Hyperbolic dynamics Renormalization Markov maps Minimal sets |
title_short |
Arc exchange systems and renormalization |
title_full |
Arc exchange systems and renormalization |
title_fullStr |
Arc exchange systems and renormalization |
title_full_unstemmed |
Arc exchange systems and renormalization |
title_sort |
Arc 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 |
dc.subject.por.fl_str_mv |
Hyperbolic dynamics Renormalization Markov maps Minimal sets |
topic |
Hyperbolic dynamics Renormalization Markov maps Minimal sets |
description |
We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010 2010-01-01T00:00:00Z 2015-10-08T14:34:48Z |
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/10400.22/6657 |
url |
http://hdl.handle.net/10400.22/6657 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
A.A. Pinto , D.A. Rand & F. Ferreira (2010) Arc exchange systems and renormalization, Journal of Difference Equations and Applications, 16:4, 347-371, DOI: 10.1080/10236190802422059 1023-6198 10.1080/10236190802422059 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Taylor & Francis |
publisher.none.fl_str_mv |
Taylor & Francis |
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 |
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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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1799131367319011328 |