PERIODIC SOLUTIONS TO HAMILTONIAN SYSTEMS WITH INFINITELY DEEP POTENTIAL WELLS

Abstract

This chapter discusses periodic solutions to Hamiltonian systems within finitely deep potential wells. Variational techniques have recently been used to obtain information concerning the existence of periodic solutions to conservative Hamiltonian systems with convex potential wells. The chapter presents an account of similar results that have been obtained for Hamiltonian systems with infinitely deep potential wells. In order to extend the theorem to higher dimensional configuration spaces Rn, it is necessary that the set S of singularities satisfy a certain geometric condition.