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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorGonchenko, Marina
dc.contributor.authorGutiérrez Serrés, Pere
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2015-05-08T11:27:07Z
dc.date.available2015-05-08T11:27:07Z
dc.date.created2014-11
dc.date.issued2014-11
dc.identifier.citationDelshams, A.; Gonchenko, M.; Gutiérrez, P. Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio. "Regular and chaotic dynamics", Novembre 2014, vol. 19, núm. 6, p. 663-680.
dc.identifier.issn1560-3547
dc.identifier.urihttp://hdl.handle.net/2117/27844
dc.description.abstractWe 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
dc.format.extent18 p.
dc.language.isoeng
dc.publisherSpringer
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.titleContinuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
dc.typeArticle
dc.subject.lemacSistemes hamiltonians
dc.subject.lemacSistemes dinàmics diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.identifier.doi10.1134/S1560354714060057
dc.relation.publisherversionhttp://link.springer.com/article/10.1134/S1560354714060057
dc.rights.accessOpen Access
drac.iddocument15343500
dc.description.versionPostprint (published version)
upcommons.citation.authorDelshams, A.; Gonchenko, M.; Gutiérrez, P.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameRegular and chaotic dynamics
upcommons.citation.volume19
upcommons.citation.number6
upcommons.citation.startingPage663
upcommons.citation.endingPage680


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