Large-Deviation Approach to Space-Time Chaos

In this Letter, we show that the analysis of Lyapunov-exponent fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a Gaussian approximation for the large-deviation function that quantifies the fluctuation probability. More precisely, a diffusion matrix D (a dynamical invariant itself) is measured and analyzed in terms of its principal components. The application of this method to three (conservative, as well as dissipative) models allows (i) quantifying the strength of the effective interactions among the different degrees of freedom, (ii) unveiling microscopic constraints such as those associated to a symplectic structure, and (iii) checking the hyperbolicity of the dynamics.