Anosov Diffeomorphisms and γ -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://hdl.handle.net/10198/15395 |
Resumo: | We consider a toral Anosov automorphism G γ : T γ → T γ given by G γ (x, y) = (ax+ y, x) in the < v, w > base, where a∈ N\ { 1 } , γ= 1 / (a+ 1 / (a+ 1 / …)) , v= (γ, 1) and w= (- 1 , γ) in the canonical base of R 2 and T γ = R 2 / (vZ× wZ). We introduce the notion of γ-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 γ ; (ii) affine classes of γ-tilings; and (iii) γ-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 γ -TilingsWe consider a toral Anosov automorphism G γ : T γ → T γ given by G γ (x, y) = (ax+ y, x) in the < v, w > base, where a∈ N\ { 1 } , γ= 1 / (a+ 1 / (a+ 1 / …)) , v= (γ, 1) and w= (- 1 , γ) in the canonical base of R 2 and T γ = R 2 / (vZ× wZ). We introduce the notion of γ-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 γ ; (ii) affine classes of γ-tilings; and (iii) γ-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences.Biblioteca Digital do IPBAlmeida, João P.Pinto, Alberto A.2018-01-31T10:00:00Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10198/15395engAlmeida, João P.; Pinto, Alberto A. (2016). Anosov Diffeomorphisms and γ -Tilings. Communications in Mathematical Physics. ISSN 0010-3616. 345, p. 435-4560010-361610.1007/s00220-016-2677-9info: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:RCAAP2023-11-21T10:35:59Zoai:bibliotecadigital.ipb.pt:10198/15395Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:04:59.883830Repositório 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 γ -Tilings |
title |
Anosov Diffeomorphisms and γ -Tilings |
spellingShingle |
Anosov Diffeomorphisms and γ -Tilings Almeida, João P. |
title_short |
Anosov Diffeomorphisms and γ -Tilings |
title_full |
Anosov Diffeomorphisms and γ -Tilings |
title_fullStr |
Anosov Diffeomorphisms and γ -Tilings |
title_full_unstemmed |
Anosov Diffeomorphisms and γ -Tilings |
title_sort |
Anosov Diffeomorphisms and γ -Tilings |
author |
Almeida, João P. |
author_facet |
Almeida, João P. Pinto, Alberto A. |
author_role |
author |
author2 |
Pinto, Alberto A. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Biblioteca Digital do IPB |
dc.contributor.author.fl_str_mv |
Almeida, João P. Pinto, Alberto A. |
description |
We consider a toral Anosov automorphism G γ : T γ → T γ given by G γ (x, y) = (ax+ y, x) in the < v, w > base, where a∈ N\ { 1 } , γ= 1 / (a+ 1 / (a+ 1 / …)) , v= (γ, 1) and w= (- 1 , γ) in the canonical base of R 2 and T γ = R 2 / (vZ× wZ). We introduce the notion of γ-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 γ ; (ii) affine classes of γ-tilings; and (iii) γ-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 2016-01-01T00:00:00Z 2018-01-31T10:00:00Z |
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/10198/15395 |
url |
http://hdl.handle.net/10198/15395 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Almeida, João P.; Pinto, Alberto A. (2016). Anosov Diffeomorphisms and γ -Tilings. Communications in Mathematical Physics. ISSN 0010-3616. 345, p. 435-456 0010-3616 10.1007/s00220-016-2677-9 |
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 |
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1799135298349694976 |