N-PULSE HOMOCLINIC ORBITS IN PERTURBATIONS OF RESONANT HAMILTONIAN-SYSTEMS

In this paper we develop an analytical method to detect orbits doubly asymptotic to slow manifolds in perturbations of integrable, two-degre e-of-freedom resonant Hamiltonian systems. Our energy-phase method app lies to both Hamiltonian and dissipative perturbations and reveals fam ilies of multi-pulse solutions which are not amenable to Melnikov-type methods. As an example, we study a two-mode approximation of the nonl inear, nonplanar oscillations of a parametrically forced inextensional beam. In this problem we find unusually complicated mechanisms for ch aotic motions and verify their existence numerically.