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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorde la Llave, Rafael
dc.contributor.authorMartínez-Seara Alonso, M. Teresa
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2013-11-20T12:48:04Z
dc.date.available2013-11-20T12:48:04Z
dc.date.created2013-06
dc.date.issued2013-06
dc.identifier.citationDelshams, A.; de la Llave, R.; Martinez-seara, M. "Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion". 2013.
dc.identifier.urihttp://hdl.handle.net/2117/20671
dc.description.abstractAbstract. We consider models given by Hamiltonians of the form H ( I;';p;q;t ; " ) = h ( I )+ n X j =1 1 2 p 2 j + V j ( q j ) + "Q ( I;';p;q;t ; " ) where I 2I R d ;' 2 T d , p;q 2 R n , t 2 T 1 . These are higher di- mensional analogues, both in the center and hyperbolic directions, of the models studied in [DLS03, DLS06a, GL06a, GL06b]. All these models present the large gap problem . We show that, for 0 < " 1, under regularity and explicit non- degeneracy conditions on the model, there are orbits whose action variables I perform rather arbitrary excursions in a domain of size O (1). This domain includes resonance lines and, hence, large gaps among d -dimensional KAM tori. The method of proof follows closely the strategy of [DLS03, DLS06a]. The main new phenomenon that appears when the di- mension d of the center directions is larger than one, is the exis- tence of multiple resonances. We show that, since these multiple resonances happen in sets of codimension greater than one in the space of actions I , they can be contoured. This corresponds to the mechanism called di usion across resonances in the Physics literature. The present paper, however, di ers substantially from [DLS03, DLS06a]. On the technical details of the proofs, we have taken advantage of the theory of the scattering map [DLS08], not avail- able when the above papers were written. We have analyzed the conditions imposed on the resonances in more detail. More precisely, we have found that there is a simple condition on the Melnikov potential which allows us to conclude that the res- onances are crossed. In particular, this condition does not depend on the resonances. So that the results are new even when applied to the models in [DLS03, DLS06a]
dc.format.extent64 p.
dc.language.isoeng
dc.relation.ispartofseries[prepr201312DelLlMS]
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.titleInstability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion
dc.typeExternal research report
dc.subject.lemacSistemes hamiltonians
dc.subject.lemacSistemes dinàmics diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.relation.publisherversionhttp://www.ma1.upc.edu/recerca/preprints/preprints-2013/Fitxers/prepr201302seara.pdf
dc.rights.accessOpen Access
local.identifier.drac12768313
dc.description.versionPreprint
local.citation.authorDelshams, A.; de la Llave, R.; Martinez-seara, M.
local.citation.publicationNameInstability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion


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