Lyapunov statistics and mixing rates for intermittent systems

Abstract

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.

7 pages, 5 figures, to appear in PRE

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Cited by in corpus (8)

• Resonances in a Chaotic Attractor Crisis of the Lorenz Flow
• On the relation between Lyapunov exponents and exponential decay of correlations
• Thermodynamic phase transitions for Pomeau-Manneville maps
• Pesin-type relation for subexponential instability
• Number of first-passage times as a measurement of information for weakly chaotic systems
• Chaotic oscillations in singularly perturbed FitzHugh-Nagumo systems
• Comment on "Lyapunov statistics and mixing rates for intermittent systems"
• Does an intermittent dynamical system remain (weakly) chaotic after drilling in a hole?