CURVATURE, TORSION, MICROCANONICAL DENSITY AND STOCHASTIC-TRANSITION

We introduce geometrical indicators (Frenet-Serret curvature and torsi on) together with microcanonical density to give evidence to the stoch astic transition of classical Hamiltonian models (Fermi-Pasta-Ulam and Lennard-Jones systems) when the specific energy grows. The transition is clearly detected through the breakdown of the harmonic-like behavi our, in combination with the vanishing of the dependence on the initia l conditions. This method of analysis presents both experimental and t heoretical advantages: it is fast and gives relatively sharp answers f or the transition; moreover, a new insight is allowed on the deformati ons and the destruction of invariant surfaces in the ordered regime. A mong the results, it is noteworthy that going from 32 to 4096 degrees of freedom the stochastic transition depends only on the specific ener gy and not on the number of degrees of freedom.