ABSTRACT
A Lyapunov1 ("lee-ah-poo-noff') exponent is a number that describes the dynamics of trajectory evolution. It capsulizes the average rate of convergence or divergence of two neighboring trajectories in phase space. Its value can be negative, zero, or positive. Negative values mean that the two trajectories draw closer to one another. Positive exponents, on the other hand, result from trajectory divergence and appear only within the chaotic domain. In other words, a positive Lyapunov exponent is one of the most important indicators of chaos. A positive Lyapunov exponent measures or quantifies sensitive dependence on initial conditions by showing the average rate (as evaluated over the entire attractor) at which two close points separate with time. Some authors refer to a Lyapunov exponent as a Lyapunov characteristic exponent (LCE) or simply a characteristic exponent. As we'll see, a dataset can have several Lyapunov exponents.
