Anosov diffeomorphisms and tilings

Bibliographic Details
Main Author: Almeida, João P.
Publication Date: 2015
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10198/17426
Summary: We consider a toral Anosov automorphism G : T → T given by G(x, y) = (ax + y; x), where a > 1 is a fixed integer, and introduce the notion of γ-tiling to prove the existence of a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms with invariant measure absolutely continuous with respect to the Lebesgue measure and topologically conjugate to G, (ii) affine classes of - tilings and (iii) solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences. This talk is based on a joint work with Alberto Pinto
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spelling Anosov diffeomorphisms and tilingsDynamical systemsAnosov diffeomorphismsTilingsWe consider a toral Anosov automorphism G : T → T given by G(x, y) = (ax + y; x), where a > 1 is a fixed integer, and introduce the notion of γ-tiling to prove the existence of a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms with invariant measure absolutely continuous with respect to the Lebesgue measure and topologically conjugate to G, (ii) affine classes of - tilings and (iii) solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences. This talk is based on a joint work with Alberto PintoBiblioteca Digital do IPBAlmeida, João P.2018-04-30T09:47:00Z20152015-01-01T00:00:00Zconference objectinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10198/17426engAlmeida, João P. (2015). Anosov diffeomorphisms and tilings. In International Workshop Progress on Difference Equations. Universidade da Beira Interior, Covilhãinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-25T12:07:32Zoai:bibliotecadigital.ipb.pt:10198/17426Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T11:34:19.018743Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Anosov diffeomorphisms and tilings
title Anosov diffeomorphisms and tilings
spellingShingle Anosov diffeomorphisms and tilings
Almeida, João P.
Dynamical systems
Anosov diffeomorphisms
Tilings
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 Almeida, João P.
author_facet Almeida, João P.
author_role author
dc.contributor.none.fl_str_mv Biblioteca Digital do IPB
dc.contributor.author.fl_str_mv Almeida, João P.
dc.subject.por.fl_str_mv Dynamical systems
Anosov diffeomorphisms
Tilings
topic Dynamical systems
Anosov diffeomorphisms
Tilings
description We consider a toral Anosov automorphism G : T → T given by G(x, y) = (ax + y; x), where a > 1 is a fixed integer, and introduce the notion of γ-tiling to prove the existence of a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms with invariant measure absolutely continuous with respect to the Lebesgue measure and topologically conjugate to G, (ii) affine classes of - tilings and (iii) solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences. This talk is based on a joint work with Alberto Pinto
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
2018-04-30T09:47:00Z
dc.type.driver.fl_str_mv conference object
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10198/17426
url http://hdl.handle.net/10198/17426
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Almeida, João P. (2015). Anosov diffeomorphisms and tilings. In International Workshop Progress on Difference Equations. Universidade da Beira Interior, Covilhã
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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