Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps

The splitting of separatrices of area preserving maps close to the identity is one of the most paradigmatic examples of an exponentially small or singular phenomenon. The intrinsic small parameter is the characteristic exponent h > 0 of the saddle fixed point. A standard technique to measure the...

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Detalhes bibliográficos
Autores: Delshams Valdés, Amadeu|||0000-0003-4134-8882, Ramírez Ros, Rafael|||0000-0002-2127-2940
Tipo de documento: artigo
Data de publicação:1999
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/771
Acesso em linha:https://hdl.handle.net/2117/771
Access Level:Acceso aberto
Palavra-chave:Dynamical systems
Bifurcation theory
Poincare-Melnikov method
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
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spelling Singular separatrix splitting and the Poincare-Melnikov method for area preserving mapsDelshams Valdés, Amadeu|||0000-0003-4134-8882Ramírez Ros, Rafael|||0000-0002-2127-2940Dynamical systemsBifurcation theoryPoincare-Melnikov methodClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systemsClassificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systemsClassificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theoryThe splitting of separatrices of area preserving maps close to the identity is one of the most paradigmatic examples of an exponentially small or singular phenomenon. The intrinsic small parameter is the characteristic exponent h > 0 of the saddle fixed point. A standard technique to measure the splitting of separatrices is the so-called Poincaré-Melnikov method, which has several specic features in the case of analytic planar maps. The aim of this talk is to compare the predictions for the splitting of separatrices provided by the Poincaré-Melnikov method, with the analytic and numerical results in a simple example where computations in multiple-precision arithmetic are performed.19991999-01-0120072007-04-26journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/771reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/7712026-05-27T15:37:01Z
dc.title.none.fl_str_mv Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
title Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
spellingShingle Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
Delshams Valdés, Amadeu|||0000-0003-4134-8882
Dynamical systems
Bifurcation theory
Poincare-Melnikov method
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
title_short Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
title_full Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
title_fullStr Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
title_full_unstemmed Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
title_sort Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
dc.creator.none.fl_str_mv Delshams Valdés, Amadeu|||0000-0003-4134-8882
Ramírez Ros, Rafael|||0000-0002-2127-2940
author Delshams Valdés, Amadeu|||0000-0003-4134-8882
author_facet Delshams Valdés, Amadeu|||0000-0003-4134-8882
Ramírez Ros, Rafael|||0000-0002-2127-2940
author_role author
author2 Ramírez Ros, Rafael|||0000-0002-2127-2940
author2_role author
dc.subject.none.fl_str_mv Dynamical systems
Bifurcation theory
Poincare-Melnikov method
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
topic Dynamical systems
Bifurcation theory
Poincare-Melnikov method
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
description The splitting of separatrices of area preserving maps close to the identity is one of the most paradigmatic examples of an exponentially small or singular phenomenon. The intrinsic small parameter is the characteristic exponent h > 0 of the saddle fixed point. A standard technique to measure the splitting of separatrices is the so-called Poincaré-Melnikov method, which has several specic features in the case of analytic planar maps. The aim of this talk is to compare the predictions for the splitting of separatrices provided by the Poincaré-Melnikov method, with the analytic and numerical results in a simple example where computations in multiple-precision arithmetic are performed.
publishDate 1999
dc.date.none.fl_str_mv 1999
1999-01-01
2007
2007-04-26
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/771
url https://hdl.handle.net/2117/771
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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