Abstract
We reexamine the multiple-time-scale method as applied to ergodic adiabatic Hamiltonian systems. Solving for the evolution of the phase space density to first order in the slowness parameter, we find a term previously overlooked. The inclusion of this term resolves a standing discrepancy 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'' systems following chaotic trajectories.
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