dc.contributor.author Delshams Valdés, Amadeu dc.contributor.author Gutiérrez Serrés, Pere dc.contributor.author Martínez-Seara Alonso, M. Teresa dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I dc.date.accessioned 2007-10-01T15:46:07Z dc.date.available 2007-10-01T15:46:07Z dc.date.issued 2003 dc.identifier.uri http://hdl.handle.net/2117/1196 dc.description.abstract We consider a singular or weakly hyperbolic Hamiltonian, with $n+1$ degrees of freedom, as a model for the behaviour of a nearly-integrable Hamiltonian near a simple resonance. The model consists of an integrable Hamiltonian possessing an $n$-dimensional hyperbolic invariant torus with fast frequencies $\omega/\sqrt\varepsilon$ and coincident whiskers, plus a perturbation of order $\mu=\varepsilon^p$. The vector $\omega$ is assumed to satisfy a Diophantine condition. We provide a tool to study, in this singular case, the splitting of the perturbed whiskers for $\varepsilon$ small enough, as well as their homoclinic intersections, using the Poincar\'e--Melnikov method. Due to the exponential smallness of the Melnikov function, the size of the error term has to be carefully controlled. So we introduce flow-box coordinates in order to take advantage of the quasiperiodicity properties of the splitting. As a direct application of this approach, we obtain quite general upper bounds for the splitting. dc.format.extent 36 pages dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 2.5 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/2.5/es/ dc.subject.lcsh Partial differential equations dc.subject.lcsh Hamiltonian dynamical systems dc.subject.lcsh Lagrangian functions dc.subject.other hyperbolic KAM theory dc.subject.other flow-box coordinates dc.subject.other Poincaré-Melnikov method dc.title Exponentially small splitting for whiskered tori in Hamiltonian systems: Flow-box coordinates and upper bounds dc.type Article dc.subject.lemac Equacions en derivades parcials dc.subject.lemac Hamilton, Sistemes de dc.subject.lemac Lagrange, Funcions de dc.contributor.group Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions dc.subject.ams Classificació AMS::35 Partial differential equations::35N Overdetermined systems dc.subject.ams Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics dc.rights.access Open Access
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