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Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a fast frequency vector $\omega/v\epsilon$, with $\epsilon=(1,\Omega)$ where $\Omega$ is an irrational number of constant type, i.e. a number whose continued fraction has bounded entries. Applying the Poincar´e–Melnikov method, we find exponentially small lower bounds for the maximal splitting distance between the stable and unstable invariant manifolds associated to the invariant torus, and we show that these bounds depend strongly on the arithmetic properties of the frequencies.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Hamiltonian systems
splitting of separatrices
Melnikov integrals
numbers of constant type
Equacions diferencials ordinàries
Sistemes dinàmics diferenciables
Attribution-NonCommercial-NoDerivs 3.0 Spain
Article - Draft

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