Mostra el registre d'ítem simple

dc.contributor.authorBaldomá Barraca, Inmaculada
dc.contributor.authorFontich, Ernest
dc.contributor.authorGuàrdia Munarriz, Marcel
dc.contributor.authorMartínez-Seara Alonso, M. Teresa
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2011-09-14T10:39:30Z
dc.date.available2011-09-14T10:39:30Z
dc.date.issued2011
dc.identifier.urihttp://hdl.handle.net/2117/13189
dc.description.abstractIn this paper we study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation which is fast and periodic in time. We provide a result valid for general systems which are polynomials or trigonometric polynomials in the state variables. Our result consists in obtaining a rigorous proof of the asymptotic formula for the measure of the splitting. We have obtained that the splitting has the asymptotic behavior K" e−a/" identifying the constants K, and a in terms of the features of the system. The study of our problem leads us to consider several cases. In some cases, assuming the per- turbation is small enough, it turns out that the values of K, coincides with the classical Melnikov approach. We have identified the limit size of the perturbation for which this classical theory holds true. However for the limit cases, which appear naturally both in averaging theory and bifurcation theory, we encounter that, generically, neither K nor are actually well predicted by Melnikov theory.
dc.format.extent117 p.
dc.language.isoeng
dc.relation.ispartofseries[prepr201101BalFGMS]
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.lcshDifferential equations
dc.subject.lcshDifferentiable dynamical systems
dc.titleExponentially small splitting of separatrices beyond Melnikov analysis: rigorous results
dc.typeExternal research report
dc.subject.lemacEquacions diferencials
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/2011/prepr201102seara.pdf
dc.rights.accessOpen Access
local.identifier.drac5910280
dc.description.versionPreprint
local.personalitzacitaciotrue


Fitxers d'aquest items

Thumbnail

Aquest ítem apareix a les col·leccions següents

Mostra el registre d'ítem simple