Periodic perturbations of Hamiltonian systems

Abstract

We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

Keywords

• periodic solutions
• poincaré–birkhoff theorem
• perturbation theory
• 34c25
• 47h15