Universality of algebraic laws in hamiltonian systems.
Hamiltonian mixed systems with unbounded phase space are typically characterized by two asymptotic algebraic laws: decay of recurrence time statistics (gamma) and superdiffusion (beta). We conjecture the universal exponents gamma=beta=3/2 for trapping of trajectories to regular islands based on our analytical results for a wide class of area-preserving maps. For Hamiltonian mixed systems with a bounded phase space the interval 3/2< or =gamma_{b}< or =3 is obtained, given that trapping takes place. A number of simulations and experiments by other authors give additional support to our claims.
Venegeroles
Roberto
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Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170, Santo André, SP, Brazil. roberto.venegeroles@ufabc.edu.br