Numerical Calculation of Lyapunov Characteristic Exponents for Smooth Dynamical Systems

Lyapunov characteristic exponents play a crucial role in characterizing the behavior of dynamical systems. They quantify the average rate at which nearby trajectories diverge or converge over time. As such, they are commonly used to assess the stability of limit sets and to detect sensitive dependence on initial conditions, that is, the presence of chaotic attractors.

This zip file contains the file lce.m, which provides a Mathematica package (compatible with version 7 or higher) for computing the Lyapunov spectrum of a smooth dynamical system. The package implements the classical algorithm introduced by Benettin et al. for estimating Lyapunov exponents in continuous- and discrete-time systems.

The zip file also includes examples.nb, a Mathematica notebook featuring several examples that illustrate how to use the main functions of the package effectively.

A detailed explanation of the theoretical background and practical use of the package is available in an article published in The Mathematica Journal, accessible at the following link:
https://library.wolfram.com/infocenter/articles/2902/