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Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.author | Gutiérrez Serrés, Pere |
dc.contributor.author | Koltsova, Oksana |
dc.contributor.author | Pacha Andújar, Juan Ramón |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2010-07-21T10:43:23Z |
dc.date.available | 2010-07-21T10:43:23Z |
dc.date.created | 2010-10 |
dc.date.issued | 2010-10 |
dc.identifier.citation | Delshams, A. [et al.]. Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method. "Regular and chaotic dynamics", Octubre 2010, vol. 15, núm. 2-3, p. 222-236. |
dc.identifier.issn | 1560-3547 |
dc.identifier.uri | http://hdl.handle.net/2117/8300 |
dc.description | hyperbolic KAM tori - transverse homoclinic orbits - Melnikov method |
dc.description.abstract | We consider a perturbation of an integrable Hamiltonian system having an equilibrium point of elliptic-hyperbolic type, having a homoclinic orbit. More precisely, we consider an (n + 2)-degree-of-freedom near integrable Hamiltonian with n centers and 2 saddles, and assume that the homoclinic orbit is preserved under the perturbation. On the center manifold near the equilibrium, there is a Cantorian family of hyperbolic KAM tori, and we study the homoclinic intersections between the stable and unstable manifolds associated to such tori. We establish that, in general, the manifolds intersect along transverse homoclinic orbits. In a more concrete model, such homoclinic orbits can be detected, in a first approximation, from nondegenerate critical points of a Mel’nikov potential. We provide bounds for the number of transverse homoclinic orbits using that, in general, the potential will be a Morse function (which gives a lower bound) and can be approximated by a trigonometric polynomial (which gives an upper bound). |
dc.format.extent | 15 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.title | Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method |
dc.type | Article |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.identifier.doi | 10.1134/S1560354710020103 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory |
dc.subject.ams | Classificació AMS::70 Mechanics of particles and systems |
dc.relation.publisherversion | http://www.springerlink.com/content/967mw8482128j74h/ |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 2514786 |
dc.description.version | Postprint (published version) |
local.citation.author | Delshams, A.; Gutiérrez, P.; Koltsova, O.; Pacha, J. |
local.citation.publicationName | Regular and chaotic dynamics |
local.citation.volume | 15 |
local.citation.number | 2-3 |
local.citation.startingPage | 222 |
local.citation.endingPage | 236 |
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