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Exponentially small splitting for the pendulum: a classical problem revisited
dc.contributor.author | Martínez-Seara Alonso, M. Teresa |
dc.contributor.author | Guàrdia Munarriz, Marcel |
dc.contributor.author | Olivé, Carme |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2010-10-14T10:14:25Z |
dc.date.available | 2010-10-14T10:14:25Z |
dc.date.created | 2010 |
dc.date.issued | 2010 |
dc.identifier.citation | Martínez-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.issn | 0938-8974 |
dc.identifier.uri | http://hdl.handle.net/2117/9688 |
dc.description.abstract | In 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.extent | 91 p. |
dc.language.iso | eng |
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.other | Exponentially small splitting of separatrices · Melnikov method · Resurgence theory · Averaging · Complex matching |
dc.title | Exponentially small splitting for the pendulum: a classical problem revisited |
dc.type | Article |
dc.subject.lemac | Equacions diferencials |
dc.subject.lemac | Sistemes dinàmics |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.identifier.doi | 10.1007/s00332-010-9068-8 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::34 Ordinary differential equations::34C Qualitative theory |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.subject.ams | Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory |
dc.relation.publisherversion | http://www.springerlink.com/content/30043804j0453783/fulltext.pdf |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 3122473 |
dc.description.version | Postprint (published version) |
local.citation.author | Martínez-Seara, M.; Guardia, M.; Olivé, C. |
local.citation.publicationName | Journal of nonlinear science |
local.citation.volume | 20 |
local.citation.number | 5 |
local.citation.startingPage | 595 |
local.citation.endingPage | 685 |
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