  An analysis of the semiclassical regime of the quantum-classical transition
is given for open, bounded, one dimensional chaotic dynamical systems.
Environmental fluctuations -- characteristic of all realistic dynamical systems
-- suppress the development of fine structure in classical phase space and damp
nonlocal contributions to the semiclassical Wigner function which would
otherwise invalidate the approximation. This dual regularization of the
singular nature of the semiclassical limit is demonstrated by a numerical
investigation of the chaotic Duffing oscillator.
