Hypothesis of strong chaos and anomalous diffusion in coupled symplectic maps

Max Planck Institute for the Physics of Complex Systems - Nöthnitzer Strasse 38, 01187 Dresden, Germany

Received: 7 November 2006
Accepted: 19 February 2007

Abstract

We investigate the high-dimensional Hamiltonian chaotic dynamics in N coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random walk inside the area corresponding to regular islands of the uncoupled maps. As a consequence, we observe long intermediate regimes of power law decay of the recurrence time statistics (with exponent ) and of ballistic motion. The asymptotic decay of correlations and anomalous diffusion depend on the stickiness of the N-dimensional invariant tori. Detailed numerical simulations show weaker stickiness for increasing N suggesting that such paradigmatic class of Hamiltonian systems asymptotically fulfill the demands of the usual hypotheses of strong chaos.