Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones

The purpose of this paper is to study phenomena in chaotic zones of area preserving maps using simpler models which are easier to analyse theoretically and numerically. First of all the study of the dynamics in a neighbourhood of the separatrices of a resonant zone is carried out. The well-known sep...

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Detalles Bibliográficos
Autores: Simó, Carles, Vieiro Yanes, Arturo
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2011
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/193842
Acceso en línea:https://hdl.handle.net/2445/193842
Access Level:acceso abierto
Palabra clave:Sistemes dinàmics hiperbòlics
Sistemes dinàmics diferenciables
Hyperbolic dynamical systems
Differentiable dynamical systems
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spelling Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zonesSimó, CarlesVieiro Yanes, ArturoSistemes dinàmics hiperbòlicsSistemes dinàmics diferenciablesHyperbolic dynamical systemsDifferentiable dynamical systemsThe purpose of this paper is to study phenomena in chaotic zones of area preserving maps using simpler models which are easier to analyse theoretically and numerically. First of all the study of the dynamics in a neighbourhood of the separatrices of a resonant zone is carried out. The well-known separatrix map, defined on a figure eight when needed, is used to determine the location of rotational invariant curves (r.i.c.) inside and outside the resonance. The interest in this part is on a quantitative description of the dynamics in a neighbourhood of the separatrices: to produce theoretical estimates of the width of the stochastic zone, distance to the r.i.c., existence of tiny islands close to the separatrices, . . . In every one of the studied items one has tried to complement the limit analytic study with realistic numerical simulations, describing the analogy when possible. After this study, we focus on the formation of larger domains without r.i.c. (e.g. Birkhoff domains). To this end we introduce the biseparatrix map model. Although this is a qualitative model, the mechanism of destruction of the "last" r.i.c., and hence the process of creation of zones without r.i.c., is clarified by means of this simple model. Several numerical examples illustrate the results obtained and are used as a test of the theoretical quantitative predictions.Elsevier B.V.2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/193842Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1016/j.physd.2010.12.005Physica D, 2011, vol. 240, num. 8, p. 732-753https://doi.org/10.1016/j.physd.2010.12.005(c) Elsevier B.V., 2011info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1938422026-05-27T06:46:51Z
dc.title.none.fl_str_mv Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
title Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
spellingShingle Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
Simó, Carles
Sistemes dinàmics hiperbòlics
Sistemes dinàmics diferenciables
Hyperbolic dynamical systems
Differentiable dynamical systems
title_short Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
title_full Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
title_fullStr Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
title_full_unstemmed Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
title_sort Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
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 Sistemes dinàmics hiperbòlics
Sistemes dinàmics diferenciables
Hyperbolic dynamical systems
Differentiable dynamical systems
topic Sistemes dinàmics hiperbòlics
Sistemes dinàmics diferenciables
Hyperbolic dynamical systems
Differentiable dynamical systems
description The purpose of this paper is to study phenomena in chaotic zones of area preserving maps using simpler models which are easier to analyse theoretically and numerically. First of all the study of the dynamics in a neighbourhood of the separatrices of a resonant zone is carried out. The well-known separatrix map, defined on a figure eight when needed, is used to determine the location of rotational invariant curves (r.i.c.) inside and outside the resonance. The interest in this part is on a quantitative description of the dynamics in a neighbourhood of the separatrices: to produce theoretical estimates of the width of the stochastic zone, distance to the r.i.c., existence of tiny islands close to the separatrices, . . . In every one of the studied items one has tried to complement the limit analytic study with realistic numerical simulations, describing the analogy when possible. After this study, we focus on the formation of larger domains without r.i.c. (e.g. Birkhoff domains). To this end we introduce the biseparatrix map model. Although this is a qualitative model, the mechanism of destruction of the "last" r.i.c., and hence the process of creation of zones without r.i.c., is clarified by means of this simple model. Several numerical examples illustrate the results obtained and are used as a test of the theoretical quantitative predictions.
publishDate 2011
dc.date.none.fl_str_mv 2011
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/193842
url https://hdl.handle.net/2445/193842
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1016/j.physd.2010.12.005
Physica D, 2011, vol. 240, num. 8, p. 732-753
https://doi.org/10.1016/j.physd.2010.12.005
dc.rights.none.fl_str_mv (c) Elsevier B.V., 2011
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Elsevier B.V., 2011
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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