Statistical Dynamics Generated by Fluctuations of Local Lyapunov Exponents

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Abstract
Fluctuation-effect of local Lyapunov exponents on the distance between two nearby trajectories is studied from a statistical-mechanical point of view. It is shown that fluctuations of the logarithmic distance between two nearby trajectories are asymptotically described as the diffusion process, if the system is chaotic, obeying the normal distribution. The diffusion coefficient is proved to be invariant under conjugation. Onset behaviors of the diffusion near two typical transition points (the accumulation point of the Feigenbaum bifurcations and the Pomeau-Manneville intermittency transition) are briefly discussed.