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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorGutiérrez Serrés, Pere
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractWe consider an example of singular or weakly hyperbolic Hamiltonian, with 3 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 a $2$-dimensional hyperbolic invariant torus with fast frequencies omega/(epsilon^(1/2)) and coincident whiskers, plus a perturbation of order mu=epsilon. We choose omega as the golden vector. Our aim is to obtain asymptotic estimates for the splitting, proving the existence of transverse intersections between the perturbed whiskers for E small enough, by applying the Poincaré-Melnikov method together with a accurate control of the size of the error term. The good arithmetic properties of the golden vector allow us to prove that the splitting function has 4 simple zeros (corresponding to nondegenerate critical points of the splitting potential), giving rise to 4~transverse homoclinic orbits. More precisely, we show that a shift of these orbits occurs when E goes across some critical values, but we establish the continuation (without bifurcations) of the 4~transverse homoclinic orbits for all values of E->0.
dc.format.extent23 pages
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshHamiltonian systems
dc.subject.lcshDifferential equations
dc.subject.otherPoincaré-Melnikov method
dc.subject.otherarithmetic properties of frequencies
dc.subject.othertransverse homoclinic orbits
dc.titleExponentially small splitting for whiskered tori in Hamiltonian systems: Continuation of transverse homoclinic orbits
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacEquacions diferencials ordinàries
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34C Qualitative theory
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.rights.accessOpen Access

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