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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorGutiérrez Serrés, Pere
dc.contributor.authorMartínez-Seara Alonso, M. Teresa
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractWe 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.extent36 pages
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshPartial differential equations
dc.subject.lcshHamiltonian dynamical systems
dc.subject.lcshLagrangian functions
dc.subject.otherhyperbolic KAM theory
dc.subject.otherflow-box coordinates
dc.subject.otherPoincaré-Melnikov method
dc.titleExponentially small splitting for whiskered tori in Hamiltonian systems: Flow-box coordinates and upper bounds
dc.subject.lemacEquacions en derivades parcials
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacLagrange, Funcions de
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::35 Partial differential equations::35N Overdetermined systems
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.rights.accessOpen Access

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