Abstract
The existence of cantori can lead to specific dynamical phenomena in non-linear systems. They represent partial barriers for the classical probability flow in phase space. We study a physical system, in which a self-similar hierarchy of cantori provides a new mechanism for 1/f-noise. In quantum systems such as the kicked quantum rotator, cantori can represent even stronger barriers and inhibit the diffusive growth of mean-square displacements. In their vicinity, the asymptotic probability distribution decays exponentially. The variation of the penetration depth across a KAM-torus is characterized by a critical exponent.
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