Planar Radial Weakly-Dissipative Diffeomorphisms

We study the effect of a small dissipative radial perturbation acting on a one parameter family of area preserving diffeomorphisms. This is a specific type of dissipative perturbation. The interest is on the global effect of the dissipation on a fixed domain around an elliptic fixed/periodic point o...

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Detalhes bibliográficos
Autores: Simó, Carles, Vieiro Yanes, Arturo
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/193917
Acesso em linha:https://hdl.handle.net/2445/193917
Access Level:acceso abierto
Palavra-chave:Homeomorfismes
Difeomorfismes
Sistemes dinàmics de baixa dimensió
Teoria ergòdica
Homeomorphisms
Diffeomorphisms
Low-dimensional dynamical systems
Ergodic theory
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spelling Planar Radial Weakly-Dissipative DiffeomorphismsSimó, CarlesVieiro Yanes, ArturoHomeomorfismesDifeomorfismesSistemes dinàmics de baixa dimensióTeoria ergòdicaHomeomorphismsDiffeomorphismsLow-dimensional dynamical systemsErgodic theoryWe study the effect of a small dissipative radial perturbation acting on a one parameter family of area preserving diffeomorphisms. This is a specific type of dissipative perturbation. The interest is on the global effect of the dissipation on a fixed domain around an elliptic fixed/periodic point of the family, rather than on the effects around a single resonance. We describe the local/global bifurcations observed in the transition from the conservative to a weakly dissipative case: the location of the resonant islands, the changes in the domains of attraction of the foci inside these islands, how the resonances disappear, etc. The possible $\omega$ -limits are determined in each case. This topological description gives rise to three different dynamical regimes according to the size of dissipative perturbation. Moreover, we determine the conservative limit of the probability of capture in a generic resonance from the interpolating flow approximation, hence assuming no homoclinics in the resonance. As a paradigm of weakly dissipative radial maps, we use a dissipative version of the Hénon map.American Institute of Physics (AIP)2023202320102023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion18 p.application/pdfhttps://hdl.handle.net/2445/193917Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: https://doi.org/10.1063/1.3515168Chaos, 2010, vol. 20, p. 1-18https://doi.org/10.1063/1.3515168(c) American Institute of Physics (AIP), 2010info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1939172026-05-29T05:05:01Z
dc.title.none.fl_str_mv Planar Radial Weakly-Dissipative Diffeomorphisms
title Planar Radial Weakly-Dissipative Diffeomorphisms
spellingShingle Planar Radial Weakly-Dissipative Diffeomorphisms
Simó, Carles
Homeomorfismes
Difeomorfismes
Sistemes dinàmics de baixa dimensió
Teoria ergòdica
Homeomorphisms
Diffeomorphisms
Low-dimensional dynamical systems
Ergodic theory
title_short Planar Radial Weakly-Dissipative Diffeomorphisms
title_full Planar Radial Weakly-Dissipative Diffeomorphisms
title_fullStr Planar Radial Weakly-Dissipative Diffeomorphisms
title_full_unstemmed Planar Radial Weakly-Dissipative Diffeomorphisms
title_sort Planar Radial Weakly-Dissipative Diffeomorphisms
dc.creator.none.fl_str_mv Simó, Carles
Vieiro Yanes, Arturo
author Simó, Carles
author_facet Simó, Carles
Vieiro Yanes, Arturo
author_role author
author2 Vieiro Yanes, Arturo
author2_role author
dc.subject.none.fl_str_mv Homeomorfismes
Difeomorfismes
Sistemes dinàmics de baixa dimensió
Teoria ergòdica
Homeomorphisms
Diffeomorphisms
Low-dimensional dynamical systems
Ergodic theory
topic Homeomorfismes
Difeomorfismes
Sistemes dinàmics de baixa dimensió
Teoria ergòdica
Homeomorphisms
Diffeomorphisms
Low-dimensional dynamical systems
Ergodic theory
description We study the effect of a small dissipative radial perturbation acting on a one parameter family of area preserving diffeomorphisms. This is a specific type of dissipative perturbation. The interest is on the global effect of the dissipation on a fixed domain around an elliptic fixed/periodic point of the family, rather than on the effects around a single resonance. We describe the local/global bifurcations observed in the transition from the conservative to a weakly dissipative case: the location of the resonant islands, the changes in the domains of attraction of the foci inside these islands, how the resonances disappear, etc. The possible $\omega$ -limits are determined in each case. This topological description gives rise to three different dynamical regimes according to the size of dissipative perturbation. Moreover, we determine the conservative limit of the probability of capture in a generic resonance from the interpolating flow approximation, hence assuming no homoclinics in the resonance. As a paradigm of weakly dissipative radial maps, we use a dissipative version of the Hénon map.
publishDate 2010
dc.date.none.fl_str_mv 2010
2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/193917
url https://hdl.handle.net/2445/193917
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1063/1.3515168
Chaos, 2010, vol. 20, p. 1-18
https://doi.org/10.1063/1.3515168
dc.rights.none.fl_str_mv (c) American Institute of Physics (AIP), 2010
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Institute of Physics (AIP), 2010
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 18 p.
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics (AIP)
publisher.none.fl_str_mv American Institute of Physics (AIP)
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.198674

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