Abstract
Hamiltonian dynamical systems with many degrees of freedom are investigated using symplectic map lattices. It is shown that anomalous diffusion exists only up to some crossover time beyond which the diffusion is normal. A diffusion constant, which is inversely proportional to the crossover time, exhibits a faster than any power-law dependence on the nonintegrability parameter, strongly suggesting the relevance of a bound by Nekhoroshev for Arnold diffusion. The motion in the standard mapping is also reexamined to show that the flicker noise is seen only down to some crossover frequency.
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