Extreme fluctuations of finite-time Lyapunov exponents in chaotic systems

Finite-time Lyapunov exponents of a chaotic attractor typically exhibit fluctuations about their asymptotic values. In computations or in experiments large fluctuations of these exponents are of concern, as they can lead to incorrect estimates of the actual exponents. We find that in common situations where a chaotic attractor contains two distinct dynamically connected components, such as one after crisis or arising in random dynamical systems, the extreme fluctuations of the finite-time exponents follow a universal, exponential distribution. We develop a physical analysis based on the random-matrix theory and provide numerical evidence to substantiate the finding.