Poincaré Recurrences in Microtron and the Global Critical Structure

Details Poincaré Recurrences in Microtron and the Global Critical Structure Poincaré Recurrences in Microtron and the Global Critical Structure

2000-06-09

arxiv.org/abs/nlin/0006013v1

Nonlinear Sciences

Chaotic Dynamics

Latex 2.09, 8 figures

Scientific paper

The mechanism of the exponential transient statistics of Poincar\'e recurrences in the presence of chaos border with its critical structure is studied using two simple models: separatrix map and the kicked rotator ('microtron'). For the exponential transient to exist the two conditions have been shown to be crucial: fast (ballistic) relaxation, and a small measure of the critical structure. The latter was found to include a new peripheral part (halo) of a surprisingly large size. First preliminary empirical evidence is presented for a new regime of Poincar\'e recurrences including the transition from exponential to exponential statistics.

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