Universality of algebraic decays in Hamiltonian systems.
Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincaré recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent.
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany.
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Cristadoro
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Ketzmerick