The Goodness of Ergodic Adiabatic Invariants

For a “slowly” time-dependent Hamiltonian system exhibiting chaotic motion that ergodically covers the energy surface, the phase space volume enclosed inside this surface is an adiabatic invariant. In this paper we examine, both numerically and theoretically, how the error in this “ergodic adiabatic invariant” scales with the slowness of the time variation of the Hamiltonian.