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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.accessioned2013-09-18T12:06:15Z
dc.date.available2013-09-18T12:06:15Z
dc.date.created2013
dc.date.issued2013
dc.identifier.citationDelshams, A.; Gonchenko, M.; Gutiérrez, P. "Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies". 2013.
dc.identifier.urihttp://hdl.handle.net/2117/20156
dc.description.abstractWe study the splitting of invariant manifolds of whiskered t ori with two or three frequencies in nearly-integrable Hamiltonian systems. We consider 2-dimensional tori with a frequency vector ω = (1 , Ω) where Ω is a quadratic irrational number, or 3-dimensional tori with a frequency v ector ω = (1 , Ω , Ω 2 ) where Ω is a cubic irrational number. Applying the Poincar ́e–Melnikov method, we find exponentia lly small asymptotic estimates for the maximal splitting distance between the stable and unstable manifolds associa ted to the invariant torus, showing that such estimates depend strongly on the arithmetic properties of the frequen cies. In the quadratic case, we use the continued fractions theory to establish a certain arithmetic property, fulfille d in 24 cases, which allows us to provide asymptotic estimate s in a simple way. In the cubic case, we focus our attention to th e case in which Ω is the so-called cubic golden number (the real root of x 3 + x − 1 = 0), obtaining also asymptotic estimates. We point out the similitudes and differences between the results obtained for both the quadratic and cubi c cases.
dc.format.extent17 p.
dc.language.isoeng
dc.relation.ispartofseries[prepr201310DelGG]
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.othersplitting of separatrices
dc.subject.otherMelnikov integrals
dc.subject.otherquadratic and cubic frequencies
dc.titleExponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies
dc.typeExternal research report
dc.subject.lemacSistemes dinàmics diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.relation.publisherversionhttps://www.ma1.upc.edu/recerca/preprints/preprints-2013/Fitxers/prepr201301gutierrez.pdf
dc.rights.accessOpen Access
drac.iddocument12762496
dc.description.versionPreprint
upcommons.citation.authorDelshams, A.; Gonchenko, M.; Gutiérrez, P.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameExponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies


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