Hyperbolicity through stable shadowing for generic geodesic flows

Bibliographic Details
Main Author: Bessa, Mário
Publication Date: 2020
Other Authors: Dias, João Lopes, Torres, M. J.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/1822/64191
Summary: We prove that the closure of the closed orbits of a generic geodesic flow on a closed Riemannian n >= 2 dimensional manifold is a uniformly hyperbolic set if the shadowing property holds C2-robustly on the metric. We obtain analogous results using weak specification and the shadowing property allowing bounded time reparametrization.
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spelling Hyperbolicity through stable shadowing for generic geodesic flowsGeodesic flowHyperbolic setsShadowingSpecificationCiências Naturais::MatemáticasScience & TechnologyWe prove that the closure of the closed orbits of a generic geodesic flow on a closed Riemannian n >= 2 dimensional manifold is a uniformly hyperbolic set if the shadowing property holds C2-robustly on the metric. We obtain analogous results using weak specification and the shadowing property allowing bounded time reparametrization.The authors were partially supported by the Project ‘New trends in Lyapunov exponents’ (PTDC/MAT-PUR/29126/2017). MB was partially supported by FCT - ‘Fundação para a Ciência e a Tecnologia’, through Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, project UID/MAT/00212/2013. JLD was partially supported by the Project CEMAPRE - UID/MULTI/00491/2019 financed by FCT/MCTES through national funds. MJT was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the Fundação para a Ciência e a Tecnologia, through the Project UID/MAT/00013/2013.ElsevierUniversidade do MinhoBessa, MárioDias, João LopesTorres, M. J.20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/64191eng0167-27891872-802210.1016/j.physd.2020.132423https://www.sciencedirect.com/science/article/abs/pii/S0167278918305967?via%3Dihubinfo: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:RCAAP2025-04-12T04:34:41Zoai:repositorium.sdum.uminho.pt:1822/64191Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T15:25:50.645673Repositórios 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 Hyperbolicity through stable shadowing for generic geodesic flows
title Hyperbolicity through stable shadowing for generic geodesic flows
spellingShingle Hyperbolicity through stable shadowing for generic geodesic flows
Bessa, Mário
Geodesic flow
Hyperbolic sets
Shadowing
Specification
Ciências Naturais::Matemáticas
Science & Technology
title_short Hyperbolicity through stable shadowing for generic geodesic flows
title_full Hyperbolicity through stable shadowing for generic geodesic flows
title_fullStr Hyperbolicity through stable shadowing for generic geodesic flows
title_full_unstemmed Hyperbolicity through stable shadowing for generic geodesic flows
title_sort Hyperbolicity through stable shadowing for generic geodesic flows
author Bessa, Mário
author_facet Bessa, Mário
Dias, João Lopes
Torres, M. J.
author_role author
author2 Dias, João Lopes
Torres, M. J.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Bessa, Mário
Dias, João Lopes
Torres, M. J.
dc.subject.por.fl_str_mv Geodesic flow
Hyperbolic sets
Shadowing
Specification
Ciências Naturais::Matemáticas
Science & Technology
topic Geodesic flow
Hyperbolic sets
Shadowing
Specification
Ciências Naturais::Matemáticas
Science & Technology
description We prove that the closure of the closed orbits of a generic geodesic flow on a closed Riemannian n >= 2 dimensional manifold is a uniformly hyperbolic set if the shadowing property holds C2-robustly on the metric. We obtain analogous results using weak specification and the shadowing property allowing bounded time reparametrization.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
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 https://hdl.handle.net/1822/64191
url https://hdl.handle.net/1822/64191
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0167-2789
1872-8022
10.1016/j.physd.2020.132423
https://www.sciencedirect.com/science/article/abs/pii/S0167278918305967?via%3Dihub
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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