\(N\)-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems (Q1894119)

The authors develop an analytical method to detect orbits doubly asymptotic to show manifolds in perturbations of integrable, two degree of freedom resonant Hamiltonian systems. The energy-phase method applies to both Hamiltonian and dissipative perturbations and reveals families of multi-pulse solutions which are not amenable to Melnikov-type methods. As an example, the authors study a two-mode approximation of the nonlinear, nonplanar oscillations of a parametrically forced inextensional beam. In this problem the authors find unusually complicated mechanisms for chaotic motions and verify their existence numerically.