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Universality of the Evolution in Paradigmatic Mixed Systems


  Or Alus [1]  ,  Shmuel Fishman [1]  ,  James D Meiss [2]  
 [1] Technion
[2] Colorado University at Boulder

For most realistic Hamiltonian systems the phase space contains both chaotic and regular orbits, mixed in a complex, fractal pattern in which islands of regular motion are surrounded by a chaotic sea. The Henon map is an example of such a system. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach. In particular transport in phase space is of great interest for dynamics, therefore the distributions of scalings fluxes through island chains were computed. The distributions of scaling of the islands' area were computed as well. Together these are used to evaluate the exponent of the decay of the survival probability in a Markov model of the dynamics.