CRM: Centro De Giorgi
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Seminari di Sistemi Dinamici e Olomorfi 2010-2011

seminar: On some universal aspects of the dynamics near invariant tori in Hamiltonian systems

speaker: Giampaolo Cristadoro (Università di Bologna)

abstract: 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. We finally dwell upon a possible relation between this conjecture and arithmetical properties of the frequency of invariant tori via Bryuno functions.

Wed 12 May, 16:00 - 17:00, Sala Riunioni del Centro De Giorgi
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