The sensitivity of a wave field's evolution to small
perturbations is of fundamental interest. For simple chaotic systems,
there are multiple distinct regimes of either exponential or Gaussian
overlap decay in time. We develop a semiclassical approach for
understanding these regimes, and give a theory that interpolates between them. The wave field's evolution is considerably more stable than the
exponential instability of chaotic trajectories seem to suggest. The
resolution of this paradox lies in the collective behavior of the
appropriate set of trajectories. Results are given for the standard map.
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