Periodic Orbits of Hamiltonian Systems

5 The Variational principles and periodic orbits 21 5.1 Lagrangian view point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2 Hamiltonian view point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.3 Fixed energy problem, the Hill’s region . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Continuation of periodic orbits as critical points . . . . . . . . . . . . . . . . . . . . 34