Chaotic dynamics with Maxima

Abstract

We present an introduction to the study of chaos in discrete and continuous dynamical systems using the CAS Maxima. These notes are intended to cover the standard topics and techniques: discrete and continuous logistic equation to model growth population, staircase plots, bifurcation diagrams and chaos transition, nonlinear continuous dynamics (Lorentz system and Duffing oscillator), Lyapunov exponents, Poincar\'e sections, fractal dimension and strange attractors. The distinctive feature here is the use of free software with just one ingredient: the CAS Maxima. It is cross-platform and have extensive on-line documentation.