Kinetic theory of area-preserving maps. Application to the standard map in the diffusive regime

摘要: The evolution of the distribution function a dynamical system governed by general two-dimensional area-preserving iterative map is studied methods nonequilibrium statistical mechanics. A closed, non-Markovian master equation determines angle-averaged (the ‘‘density profile’’). complementary, angle-dependent part (‘‘the fluctuations’’) expressed as functional density profile. Whenever there exist two widely separated intrinsic time scales, can be markovianized, yielding an asymptotic kinetic equation. theory applied to standard in diffusive regime, i.e., for large stochasticity parameter and scale length. written solved analytically this approximation. characteristic scales are exhibited. This permits thorough study profile, its tendency toward Markovian approximation, eventually Gaussian packet. fluctuations also described detail. various relaxation processes asymptotically single diffusion coefficient, which calculated analytically. model appears testing bench equations. previous approaches problem reviewed critically discussed.