3 years ago

Correlation dimension and Lyapunov exponent via extreme value theory.

Davide Faranda, Sandro Vaienti

We show how to obtain theoretical and numerical estimates of correlation dimension and Lyapunov exponents by using the extreme value theory. Maxima of suitable observables sampled along the trajectory of a chaotic dynamical system converge asymptotically to classical extreme value laws where: i) the inverse of the scale parameter gives the correlation dimension, ii) the extremal index is related to positive Lyapunov exponents. Numerical estimates are straightforward to obtain as they imply just a simple fit to an univariate distribution. The estimates of the Lyapunov exponents are particularly robust even with relatively short time series.

Publisher URL: http://arxiv.org/abs/1711.03021

DOI: arXiv:1711.03021v1

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