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 Títol: Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing Autor: Delshams Valdés, Amadeu ; Gelfreich, Vassili; Jorba, Angel ; Martínez-Seara Alonso, M. Teresa Data: 1997 Tipus de document: Article Resum: Quasiperiodic perturbations with two frequencies $(1/\varepsilon ,\gamma /\varepsilon )$ of a pendulum are considered, where $\gamma$ is the golden mean number. We study the splitting of the three-dimensional invariant manifolds associated to a two-dimensional invariant torus in a neighbourhood of the saddle point of the pendulum. Provided that some of the Fourier coefficients of the perturbation (the ones associated to Fibonacci numbers) are separated from zero, it is proved that the invariant manifolds split for $\varepsilon$ small enough. The value of the splitting, that turns out to be ${\rm O} (\exp (-{\rm const} /\sqrt{\varepsilon }) )$, is correctly predicted by the Melnikov function. URI: http://hdl.handle.net/2117/879 Apareix a les col·leccions: EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions. Articles de revistaDepartaments de Matemàtica Aplicada. Articles de revista Comparteix: