High precision numerical estimation of the largest Lyapunov exponent

A numerical algorithm for estimating the largest Lyapunov exponent of a chaotic attractor is presented. The method makes use of the minimal time for two trajectories to diverge beyond a given distance from each other. We define the nth divergence speed G ( n ) and show that, for an appropriate range of n, the largest Lyapunov exponent can be approximated by G ( n ) .