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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.accessioned2014-04-24T09:32:24Z
dc.date.available2014-04-24T09:32:24Z
dc.date.created2014-02
dc.date.issued2014-02
dc.identifier.citationDelshams, A.; Gonchenko, M.; Gutiérrez, P. "Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type". 2014.
dc.identifier.urihttp://hdl.handle.net/2117/22687
dc.description.abstractWe study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a fast frequency vector $\omega/v\epsilon$, with $\epsilon=(1,\Omega)$ where $\Omega$ is an irrational number of constant type, i.e. a number whose continued fraction has bounded entries. Applying the Poincar´e–Melnikov method, we find exponentially small lower bounds for the maximal splitting distance between the stable and unstable invariant manifolds associated to the invariant torus, and we show that these bounds depend strongly on the arithmetic properties of the frequencies.
dc.format.extent12 p.
dc.language.isoeng
dc.relation.ispartofseries[prepr201401DelGG]
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.lcshHamiltonian systems
dc.subject.othersplitting of separatrices
dc.subject.otherMelnikov integrals
dc.subject.othernumbers of constant type
dc.titleExponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type
dc.typeExternal research report
dc.subject.lemacEquacions diferencials ordinàries
dc.subject.lemacSistemes dinàmics 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.iddocument13041856
dc.description.versionPreprint
upcommons.citation.authorDelshams, A.; Gonchenko, M.; Gutiérrez, P.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameExponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type


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