Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio

We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number Ω = √ 2 − 1. We show that t...

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Detalhes bibliográficos
Autores: Delshams Valdés, Amadeu|||0000-0003-4134-8882, Gonchenko, Marina, Gutiérrez Serrés, Pere|||0000-0001-8027-1166
Formato: artículo
Fecha de publicación:2014
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/27844
Acesso em linha:https://hdl.handle.net/2117/27844
https://dx.doi.org/10.1134/S1560354714060057
Access Level:acceso abierto
Palavra-chave:Sistemes hamiltonians
Sistemes dinàmics diferenciables
Àrees temàtiques de la UPC::Matemàtiques i estadística
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repository_id_str
spelling Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratioDelshams Valdés, Amadeu|||0000-0003-4134-8882Gonchenko, MarinaGutiérrez Serrés, Pere|||0000-0001-8027-1166Sistemes hamiltoniansSistemes dinàmics diferenciablesÀrees temàtiques de la UPC::Matemàtiques i estadísticaWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number Ω = √ 2 − 1. We show that the Poincar ́ e – Melnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic estimates for the transversality of the splitting whose dependence on the perturbation parameter ε satisfies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of ε , generalizing the results previously known for the golden numberSpringer20142014-11-0120152015-05-08journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/27844https://dx.doi.org/10.1134/S1560354714060057reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/278442026-05-27T15:37:01Z
dc.title.none.fl_str_mv Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
title Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
spellingShingle Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
Delshams Valdés, Amadeu|||0000-0003-4134-8882
Sistemes hamiltonians
Sistemes dinàmics diferenciables
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
title_full Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
title_fullStr Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
title_full_unstemmed Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
title_sort Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
dc.creator.none.fl_str_mv Delshams Valdés, Amadeu|||0000-0003-4134-8882
Gonchenko, Marina
Gutiérrez Serrés, Pere|||0000-0001-8027-1166
author Delshams Valdés, Amadeu|||0000-0003-4134-8882
author_facet Delshams Valdés, Amadeu|||0000-0003-4134-8882
Gonchenko, Marina
Gutiérrez Serrés, Pere|||0000-0001-8027-1166
author_role author
author2 Gonchenko, Marina
Gutiérrez Serrés, Pere|||0000-0001-8027-1166
author2_role author
author
dc.subject.none.fl_str_mv Sistemes hamiltonians
Sistemes dinàmics diferenciables
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Sistemes hamiltonians
Sistemes dinàmics diferenciables
Àrees temàtiques de la UPC::Matemàtiques i estadística
description We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number Ω = √ 2 − 1. We show that the Poincar ́ e – Melnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic estimates for the transversality of the splitting whose dependence on the perturbation parameter ε satisfies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of ε , generalizing the results previously known for the golden number
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-11-01
2015
2015-05-08
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/27844
https://dx.doi.org/10.1134/S1560354714060057
url https://hdl.handle.net/2117/27844
https://dx.doi.org/10.1134/S1560354714060057
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 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/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 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 15.300719

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