On universality of algebraic decays in Hamiltonian systems

Abstract

Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincare' 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.

4 pages, 3 figures

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• Long-Time Correlations in the Stochastic Regime
• Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space
• Average exit times in volume preserving maps
• Algebraic decay in hierarchical graphs

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