Mostra el registre d'ítem simple
Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.author | de la Llave, Rafael |
dc.contributor.author | Martínez-Seara Alonso, M. Teresa |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2013-11-20T12:48:04Z |
dc.date.available | 2013-11-20T12:48:04Z |
dc.date.created | 2013-06 |
dc.date.issued | 2013-06 |
dc.identifier.citation | Delshams, A.; de la Llave, R.; Martinez-seara, M. "Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion". 2013. |
dc.identifier.uri | http://hdl.handle.net/2117/20671 |
dc.description.abstract | Abstract. 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.extent | 64 p. |
dc.language.iso | eng |
dc.relation.ispartofseries | [prepr201312DelLlMS] |
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.lcsh | Hamiltonian systems |
dc.title | Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion |
dc.type | External research report |
dc.subject.lemac | Sistemes hamiltonians |
dc.subject.lemac | Sistemes dinàmics diferenciables |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.relation.publisherversion | http://www.ma1.upc.edu/recerca/preprints/preprints-2013/Fitxers/prepr201302seara.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 12768313 |
dc.description.version | Preprint |
local.citation.author | Delshams, A.; de la Llave, R.; Martinez-seara, M. |
local.citation.publicationName | Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion |
Fitxers d'aquest items
Aquest ítem apareix a les col·leccions següents
-
Reports de recerca [103]
-
Reports de recerca [403]