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Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.author | Gonchenko, Marina |
dc.contributor.author | Gutiérrez Serrés, Pere |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2014-09-23T09:33:01Z |
dc.date.available | 2014-09-23T09:33:01Z |
dc.date.created | 2014-09 |
dc.date.issued | 2014-09 |
dc.identifier.citation | Delshams, 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.uri | http://hdl.handle.net/2117/24138 |
dc.description.abstract | 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 $\Omega=\sqrt2-1$. 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.extent | 17 p. |
dc.language.iso | eng |
dc.relation.ispartofseries | [prepr201404DelGG] |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Invariant manifolds |
dc.subject.other | transverse homoclinic orbits |
dc.subject.other | splitting of separatrices |
dc.subject.other | Melnikov integrals |
dc.subject.other | silver ratio |
dc.title | Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio |
dc.type | External research report |
dc.subject.lemac | Sistemes dinàmics diferenciables |
dc.subject.lemac | Equacions diferencials ordinàries |
dc.subject.lemac | Varietats diferenciables |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.relation.publisherversion | http://www.ma1.upc.edu/recerca/preprints/preprints-2014/preprint-2014 |
dc.rights.access | Open Access |
local.identifier.drac | 15182795 |
dc.description.version | Preprint |
local.citation.author | Delshams, A.; Gonchenko, M.; Gutiérrez, P. |
local.citation.publicationName | Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio |
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