Periodic orbits of certain Hénon-like maps
We prove that the Poincaré map has at least fixed points (whose trajectories are contained inside the segment W) where the homeomorphism is given by the segment W.
By using the least action principle and minimax methods in critical point theory, some existence theorems for periodic solutions of second order Hamiltonian systems are obtained.
Two theorems about the existence of periodic solutions with prescribed energy for second order Hamiltonian systems are obtained. One gives existence for almost all energies under very natural conditions. The other yields existence for all energies under a further condition.