Normal and Anomalous Diffusion in a Deterministic Area-preserving Map

Abstract

Chaotic deterministic dynamics of a particle can give rise to diffusive Brownian motion. In this paper, we compute analytically the diffusion coefficient for a particular two-dimensional stochastic layer induced by the kicked Harper map. The variations of the transport coefficient as a parameter is varied are analyzed in terms of the underlying classical trajectories with particular emphasis in the appearance and bifurcations of periodic orbits. When accelerator modes are present, anomalous diffusion of the L\'evy type can occur. The exponent characterizing the anomalous diffusion is computed numerically and analyzed as a function of the parameter.