On the Number of Periodic Trajectories for a Hamiltonian Flow on a Convex Energy Surface

Abstract

kbstract In this paper, we look for periodic solutions, with prescribed energy h C of Hamilton's equations: (H) a H (x, p), p aH (x, p). ap Ax It is assumed that the Hamiltonian H is convex on R x R, and that the origin (0, 0) is an isolated equilibrium. It is also assumed that some ball B around the origin can be found such that the energy surface H'(h) lies outside B but inside v'2 B. Under these assumptions, we prove that there are at least n distinct periodic orbits of the Hamiltonian flow (H) with energy level h.