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 $\gamma =\beta =3\mathrm{/}2$ 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 $3\mathrm{/}2\le {\gamma }_b\le 3$ was obtained, given that trapping takes place. A number of simulations and experiments by other authors give additional support to our claims.