Homoclinic solutions of Hamiltonian systems with symmetry

Gianni Arioli Dipartimento di Scienze e Tecnologie Avanzate via Cavour 84 15100 Alessandria Italy

                gianni@mfn.al.unipmn.it

The existence of infinitely many homoclinic solutions for a first order Hamiltonian system, symmetric with respect to an action of a compact Lie group is proved by means of variational methods. No convexity assumptions on the Hamiltonian are made.