96-400 Rothos V.M., Bountis T.

Mel'nikov's Vector and Singularity Analysis of N DOF Hamiltonian Systems (29K, LaTeX) Sep 7, 96

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Abstract. We investigate periodically perturbed, integrable 2 degree of freedom (d.o.f.) Hamiltonian systems as a paradigm of the dynamics of 3 d.o.f. Hamiltonian systems. We derive the Mel'nikov vector, determining transversal intersections of the invariant manifolds of a saddle fixed point of the associated (time-periodic) map and investigate its connection with the breakdown of the Painlev\'e property of the unperturbed solutions in complex time.

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