Universality of algebraic laws in Hamiltonian systems

2008/12/31 by Roberto Venegeroles · 1 citation
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1103/physrevlett.102.064101

published as Phys. Rev. Lett. 102, 064101 (2009) · 4 pages, revised version

arxiv created 2009/02/10 · arxiv updated 2009/12/01

Abstract

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≤γ_b≤3 was obtained, given that trapping takes place. A number of simulations and experiments by other authors give additional support to our claims.

Cited by

• Hierarchical fragmentation of regular islands in a discontinuous nontwist map