Poincaré-Birkhoff periodic orbits for mechanical Hamiltonian systems on T T n

Here, a version of the Arnol’d conjecture, first studied by Conley and Zehnder, giving a generalization of the Poincaré-Birkhoff last geometrical theorem, is proved inside Viterbo’s framework of the generating functions quadratic at infinity. We give brief overviews of some tools that are often utilized in symplectic topology.