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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.accessioned2014-09-23T09:33:01Z
dc.date.available2014-09-23T09:33:01Z
dc.date.created2014-09
dc.date.issued2014-09
dc.identifier.citationDelshams, A.; Gonchenko, M.; Gutiérrez, P. "Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio". 2014.
dc.identifier.urihttp://hdl.handle.net/2117/24138
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 $\Omega=\sqrt2-1$. We show that the oincare-Melnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisffies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilon
dc.format.extent17 p.
dc.language.isoeng
dc.relation.ispartofseries[prepr201404DelGG]
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.subject.lcshInvariant manifolds
dc.subject.othertransverse homoclinic orbits
dc.subject.othersplitting of separatrices
dc.subject.otherMelnikov integrals
dc.subject.othersilver ratio
dc.titleContinuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
dc.typeExternal research report
dc.subject.lemacSistemes dinàmics diferenciables
dc.subject.lemacEquacions diferencials ordinàries
dc.subject.lemacVarietats diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.relation.publisherversionhttp://www.ma1.upc.edu/recerca/preprints/preprints-2014/preprint-2014
dc.rights.accessOpen Access
drac.iddocument15182795
dc.description.versionPreprint
upcommons.citation.authorDelshams, A.; Gonchenko, M.; Gutiérrez, P.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameContinuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio


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