Finite size Lyapunov exponent: review on applications

In dynamical systems, the growth of infinitesimal perturbations is well characterized by the Lyapunov exponents. In many situations of interest, however, important phenomena involve finite amplitude perturbations, which are ruled by nonlinear dynamics out of tangent space, and thus cannot be captured by the standard Lyapunov exponents. We review the application of the finite size Lyapunov exponent (FSLE) for the characterization of noninfinitesimal perturbations in a variety of systems. In particular, we illustrate their usage in the context of predictability of systems with multiple spatiotemporal scales of geophysical relevance, in the characterization of nonlinear instabilities, and in some aspects of transport in fluid flows. We also discuss the application of the FSLE to more general aspects such as chaos-noise detection and coarse-grained descriptions of signals. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. PACS numbers: 05.45.−a, 05.45.Pq, 47.27.ed (Some figures may appear in colour only in the online journal)