MULTIPLE-TIME-SCALE APPROACH TO ERGODIC ADIABATIC SYSTEMS - ANOTHER LOOK

We reexamine the multiple-time-scale method as applied to ergodic adia batic Hamiltonian systems. Solving for the evolution of the phase spac e density to first order in the slowness parameter, we find a term pre viously overlooked. The inclusion of this term resolves a standing dis crepancy between the multiple-time-scale approach to this problem, and an approach using a Fokker-Planck equation. We apply our solution to the dynamics of a ''slow'' system coupled to an ensemble of ''fast'' s ystems following chaotic trajectories.