Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems

Details Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems

2001-08-09

arxiv.org/abs/nlin/0108016v1

Nonlinear Sciences

Chaotic Dynamics

6 pages, 3 figures, submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.88.054103

The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach for understanding both regimes, and give a simple expression for the crossover time between the regimes. 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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