Semi-classical behaviour of Schr\"odinger's dynamics : revivals of wave packets on hyperbolic trajectory

The aim of this paper is to study the semi-classical behaviour of Schr"odinger’s dynamics for an one-dimesional quantum Hamiltonian with a classical hyperbolic trajectory. As in the regular case (elliptic trajectory), we prove, that for an initial wave packets localized in energy, the dynamics follows the classical motion during short time. And, for large time, a new period for the dynamics appears : the wave packets revivals.