Lyapunov statistics and mixing rates for intermittent systems

Details Lyapunov statistics and mixing rates for intermittent systems Lyapunov statistics and mixing rates for intermittent systems

2011-07-11

arxiv.org/abs/1107.2077v2

Phys. Rev. E84, 066210 (2011)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 5 figures, to appear in PRE

Scientific paper

10.1103/PhysRevE.84.066210

We consider here a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems. We demonstrate that this conjecture fails for a generic class of maps of the Pomeau-Manneville type. We show further that, typically, the decay properties of such tail probabilities do not provide significant information on key aspects of weakly chaotic dynamics such as ergodicity and instability regimes. Our approaches are firmly based on rigorous results, particularly the Aaronson-Darling-Kac theorem, and are also confirmed by exhaustive numerical simulations.

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