Homoclinic and heteroclinic orbits for a class of Hamiltonian systems

The existence of a rich structure of homoclinic and heteroclinic solutions is established for a family of Hamiltonian systems that serve as a simpler model for the multiple pendulum system. The proof is based on recently developed arguments from the calculus of variations that have proved useful in finding actual solutions of an equation near approximate solution.This research was sponsorted in part by the National Science Foundation under grant #MCS-8110556 and the U. S. Army Research Office under Contract #DAAL03-87-K-0043. Any reproduction for the purpose of the United States Government is permitted.