A large-deviation approach to space-time chaos

Abstract

In this Letter we show that the analysis of Lyapunov-exponents 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 $\mathbf{D}$ (a dynamical invariant itself) is measured and analysed 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; (iii) checking the hyperbolicity of the dynamics.

4 pages, 3 figures. To appear in Phys. Rev. Lett

References in corpus (4)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Characterizing dynamics with covariant Lyapunov vectors
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Hyperbolicity and the effective dimension of spatially-extended dissipative systems

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