Stochasticity threshold for classical Hamiltonian systems

Summary

We consider a class of Hamiltonian systems that show chaoticity and give a recipe to get their stochasticity threshold. When the multiple time scale perturbation analysis (MTSA) is applied, a set of differential equations is obtained for corrections to first order in the perturbation strength. The stability analysis of them gives an infinite set of saddle points for the amplitude and phase of motion and a time scale on which the information on initial conditions goes lost. The comparison with the proper orbital time gives the stochasticity threshold. The mechanism is applied to a modified version of the well-known Henon-Heiles model.