Universality of algebraic laws in Hamiltonian systems
英文摘要：
Hamiltonian mixed systems with unbounded phase space are typically characterized by two asymptotic algebraic laws: decay of recurrence time statistics ($γ$) and superdiffusion ($β$). We conjecture the universal exponents $γ=β=3/2$ 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 bounded phase space the interval $3/2\leqγ_{b}\leq3$ was obtained, given that trapping takes place. A number of simulations and experiments by other authors give additional support to our claims.
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