Instability statistics and mixing rates

Abstract

We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of polynomial decay rates of time correlations and Poincaré recurrences in the -quite delicate- case of dynamical systems with weak chaotic properties.

5 pages, 5 figures

References in corpus (7)

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• Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems
• Lyapunov statistics and mixing rates for intermittent systems
• Exploring conservative islands using correlated and uncorrelated noise
• Numerical estimate of infinite invariant densities: application to Pesin-type identity
• PageRank model of opinion formation on Ulam networks
• Intermittent stickiness synchronization
• Importance Sampling of Rare Events in Chaotic Systems
• Estimating hyperbolicity of chaotic bidimensional maps
• Fluctuations in quantum one-dimensional thermostatted systems with off-diagonal disorder
• $1/f$ Spectrum and 1-Stable Law in One-Dimensional Intermittent Map with Uniform Invariant Measure and Nekhoroshev Stability
• On stable laws in a one-dimensional intermittent map equipped with a uniform invariant measure
• Anomalous dynamics and the choice of Poincaré recurrence-set
• Comment on "Lyapunov statistics and mixing rates for intermittent systems"
• Oseledets' Splitting of Standard-like Maps