Universality of algebraic laws in Hamiltonian systems

Details Universality of algebraic laws in Hamiltonian systems Universality of algebraic laws in Hamiltonian systems

2008-12-11

arxiv.org/abs/0812.2271v2

Phys. Rev. Lett. 102, 064101 (2009)

Nonlinear Sciences

Chaotic Dynamics

4 pages, revised version

Scientific paper

10.1103/PhysRevLett.102.064101

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 bounded phase space the interval $3/2\leq\gamma_{b}\leq3$ 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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