Abstract

We present a method to calculate Lyapunov exponents of an attractor of a discrete dynamical system using spatial averages rather than time averages. This involves determining directions at every point which, averaged over the attractor, stretch at rates given by the Lyapunov exponents. Our approach may be useful when the dynamical system is being reconstructed from a finite set of data. Here we triangulate the data points; the triangulation both makes the spatial averaging process finite and allows the calculation of an invariant measure, so that contributions to the exponents from different regions of phase space may be weighted correctly.