Hypothesis of strong chaos and anomalous diffusion in coupled symplectic maps

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 $\gamma =0.5$) 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