11-17 Inmaculada Baldoma, Ernest Fontich, Marcel Guardia and Tere M. Seara

Exponentially small splitting of separatrices for one and a half degrees of freedom Hamiltonian systems (1754K, Postscript) Feb 8, 11

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Abstract. In this paper we study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation which is fast and periodic in time. We provide the asymptotic formula for the measure of the splitting for both the so-called regular and singular cases. In the latter we show that Melnikov theory fails to predict correctly the first order of the splitting of separatrices.

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