Estimation of surrogate measure for the largest Lyapunov exponent from the information entropy of symbolic dynamics

A positive Lyapunov exponent is the most convincing signature of chaos. However, existing methods for estimating the Lyapunov exponent from a time series often give unreliable estimates because they trace the time evolution of the distance between a pair of initially neighboring trajectories in phase space. Here, we propose a mathematical method for estimating a surrogate measure for the Lyapunov exponent from the information entropy of a symbolic time series without tracing initially neighboring trajectories. We apply the proposed method to numerical and experimental time series to verify its validity.