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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorGonçalves Schaefer, Rodrigo
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2017-05-17T07:57:57Z
dc.date.available2017-05-17T07:57:57Z
dc.date.issued2017-01-01
dc.identifier.citationDelshams, A., Gonçalves, R. Arnold diffusion for a complete family of perturbations. "Regular and chaotic dynamics", 1 Gener 2017, vol. 22, núm. 1, p. 78-108.
dc.identifier.issn1560-3547
dc.identifier.urihttp://hdl.handle.net/2117/104532
dc.description.abstractIn this work we illustrate the Arnold diffusion in a concrete example — the a priori unstable Hamiltonian system of 2 + 1/2 degrees of freedom H(p, q, I, f, s) = p2/2+ cos q - 1 + I2/2 + h(q, f, s; e) — proving that for any small periodic perturbation of the form h(q, f, s; e) = e cos q (a00 + a10 cosf + a01 cos s) (a10a01 ¿ 0) there is global instability for the action. For the proof we apply a geometrical mechanism based on the so-called scattering map. This work has the following structure: In the first stage, for a more restricted case (I* ~ p/2µ, µ = a10/a01), we use only one scattering map, with a special property: the existence of simple paths of diffusion called highways. Later, in the general case we combine a scattering map with the inner map (inner dynamics) to prove the more general result (the existence of instability for any µ). The bifurcations of the scattering map are also studied as a function of µ. Finally, we give an estimate for the time of diffusion, and we show that this time is primarily the time spent under the scattering map.
dc.format.extent31 p.
dc.language.isoeng
dc.publisherSpringer
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.lcshHamiltonian systems
dc.subject.lcshDifferentiable dynamical systems
dc.subject.otherArnold diffusion
dc.subject.othernormally hyperbolic invariant manifolds
dc.subject.otherscattering maps
dc.titleArnold diffusion for a complete family of perturbations
dc.typeArticle
dc.subject.lemacSistemes hamiltonians
dc.subject.lemacSistemes dinàmics diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.identifier.doi10.1134/S1560354717010051
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttp://link.springer.com/article/10.1134%2FS1560354717010051
dc.rights.accessOpen Access
local.identifier.drac19826182
dc.description.versionPostprint (published version)
local.citation.authorDelshams, A.; Gonçalves, R.
local.citation.publicationNameRegular and chaotic dynamics
local.citation.volume22
local.citation.number1
local.citation.startingPage78
local.citation.endingPage108


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