Nonintegrability and fractional kinetics along filamented surfaces

Abstract

Filamented surfaces are invariant surfaces, with respect to the Hamiltonian dynamics, that are wound by trajectories and that have topological genus more than one. Dynamics along the surfaces is not integrable (V. Kozlov, 1979), and numerous examples of such surfaces can be found in hydro- and magneto-hydrodynamics. Using the renormalization group approach we study transport of particles along such surfaces and show that the kinetics is superdiffusive. Other discussed features of the dynamics are Poincaré recurrences, stickiness of trajectories, and connection to dynamics in billiards. © 2008 Springer.