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dc.contributor.authorMartínez-Seara Alonso, M. Teresa
dc.contributor.authorGuàrdia Munarriz, Marcel
dc.contributor.authorOlivé, Carme
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2010-10-14T10:14:25Z
dc.date.available2010-10-14T10:14:25Z
dc.date.created2010
dc.date.issued2010
dc.identifier.citationMartínez-Seara, M.; Guardia, M.; Olivé, C. Exponentially small splitting for the pendulum: a classical problem revisited. "Journal of nonlinear science", 2010, vol. 20, núm. 5, p. 595-685.
dc.identifier.issn0938-8974
dc.identifier.urihttp://hdl.handle.net/2117/9688
dc.description.abstractIn this paper, we study the classical problem of the exponentially small splitting of separatrices of the rapidly forced pendulum. Firstly, we give an asymptotic formula for the distance between the perturbed invariant manifolds in the so-called singular case and we compare it with the prediction of Melnikov theory. Secondly, we give exponentially small upper bounds in some cases in which the perturbation is bigger than in the singular case and we give some heuristic ideas how to obtain an asymptotic formula for these cases. Finally, we study how the splitting of separatrices behaves when the parameters are close to a codimension-2 bifurcation point.
dc.format.extent91 p.
dc.language.isoeng
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.otherExponentially small splitting of separatrices · Melnikov method · Resurgence theory · Averaging · Complex matching
dc.titleExponentially small splitting for the pendulum: a classical problem revisited
dc.typeArticle
dc.subject.lemacEquacions diferencials
dc.subject.lemacSistemes dinàmics
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.identifier.doi10.1007/s00332-010-9068-8
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34C Qualitative theory
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34E Asymptotic theory
dc.relation.publisherversionhttp://www.springerlink.com/content/30043804j0453783/fulltext.pdf
dc.rights.accessRestricted access - publisher's policy
local.identifier.drac3122473
dc.description.versionPostprint (published version)
local.citation.authorMartínez-Seara, M.; Guardia, M.; Olivé, C.
local.citation.publicationNameJournal of nonlinear science
local.citation.volume20
local.citation.number5
local.citation.startingPage595
local.citation.endingPage685


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