Approach to Gaussian stochastic behavior for systems driven by deterministic chaotic forces.
We consider skew-product dynamical systems that describe the stroboscopic dynamics of a damped particle subjected to a chaotic kick force. In a suitable scaling limit the dynamics converges to the Ornstein-Uhlenbeck process. We investigate the deterministic chaotic corrections in the vicinity of this Gaussian limit case for various examples of chaotic forces. We present numerical evidence that, for certain classes of chaotic forces, the deterministic chaotic corrections of the invariant density are universal. We provide analytical results for forces generated by Tchebyscheff maps and sketch a renormalization group theory in the space of probability densities.
Hilgers
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Institut für Theoretische Physik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany.
Beck
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C