Anosov Diffeomorphisms and -Tilings
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://repositorio.inesctec.pt/handle/123456789/6131 http://dx.doi.org/10.1007/s00220-016-2677-9 |
Resumo: | We consider a toral Anosov automorphism G(gamma) : T-gamma --> T-gamma given by G(gamma) (x, y) = (ax + y, x) in the < v, w > base, where , a is an element of N\{1}, gamma = 1/(a + 1/(a + 1/...)), v = (gamma, 1) and w = (-1, gamma) in the canonical base of R-2 and T-gamma = R-2 / (vZ x wZ). We introduce the notion of gamma-tilings to prove the existence of a one-to-one correspondence between (i) marked smooth conjugacy classes of Anosov diffeomorphisms, with invariant measures absolutely continuous with respect to the Lebesgue measure, that are in the isotopy class of G(gamma); (ii) affine classes of gamma-tilings; and (iii) gamma-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Anosov Diffeomorphisms and -TilingsWe consider a toral Anosov automorphism G(gamma) : T-gamma --> T-gamma given by G(gamma) (x, y) = (ax + y, x) in the < v, w > base, where , a is an element of N\{1}, gamma = 1/(a + 1/(a + 1/...)), v = (gamma, 1) and w = (-1, gamma) in the canonical base of R-2 and T-gamma = R-2 / (vZ x wZ). We introduce the notion of gamma-tilings to prove the existence of a one-to-one correspondence between (i) marked smooth conjugacy classes of Anosov diffeomorphisms, with invariant measures absolutely continuous with respect to the Lebesgue measure, that are in the isotopy class of G(gamma); (ii) affine classes of gamma-tilings; and (iii) gamma-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences.2018-01-15T12:17:10Z2016-01-01T00:00:00Z2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://repositorio.inesctec.pt/handle/123456789/6131http://dx.doi.org/10.1007/s00220-016-2677-9engJoão Paulo AlmeidaAlberto Pintoinfo: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:RCAAP2023-05-15T10:20:49Zoai:repositorio.inesctec.pt:123456789/6131Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:53:40.383334Repositório 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 |
Anosov Diffeomorphisms and -Tilings |
title |
Anosov Diffeomorphisms and -Tilings |
spellingShingle |
Anosov Diffeomorphisms and -Tilings João Paulo Almeida |
title_short |
Anosov Diffeomorphisms and -Tilings |
title_full |
Anosov Diffeomorphisms and -Tilings |
title_fullStr |
Anosov Diffeomorphisms and -Tilings |
title_full_unstemmed |
Anosov Diffeomorphisms and -Tilings |
title_sort |
Anosov Diffeomorphisms and -Tilings |
author |
João Paulo Almeida |
author_facet |
João Paulo Almeida Alberto Pinto |
author_role |
author |
author2 |
Alberto Pinto |
author2_role |
author |
dc.contributor.author.fl_str_mv |
João Paulo Almeida Alberto Pinto |
description |
We consider a toral Anosov automorphism G(gamma) : T-gamma --> T-gamma given by G(gamma) (x, y) = (ax + y, x) in the < v, w > base, where , a is an element of N\{1}, gamma = 1/(a + 1/(a + 1/...)), v = (gamma, 1) and w = (-1, gamma) in the canonical base of R-2 and T-gamma = R-2 / (vZ x wZ). We introduce the notion of gamma-tilings to prove the existence of a one-to-one correspondence between (i) marked smooth conjugacy classes of Anosov diffeomorphisms, with invariant measures absolutely continuous with respect to the Lebesgue measure, that are in the isotopy class of G(gamma); (ii) affine classes of gamma-tilings; and (iii) gamma-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-01-01T00:00:00Z 2016 2018-01-15T12:17:10Z |
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://repositorio.inesctec.pt/handle/123456789/6131 http://dx.doi.org/10.1007/s00220-016-2677-9 |
url |
http://repositorio.inesctec.pt/handle/123456789/6131 http://dx.doi.org/10.1007/s00220-016-2677-9 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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.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 |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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 |
repository.mail.fl_str_mv |
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1799131610538311680 |