Chaos theory

Summary

Chaos theory studies deterministic dynamical systems whose long-time behaviour looks random and cannot be predicted in practice. The key feature is sensitive dependence on initial conditions, the butterfly effect: tiny differences in the starting state grow until they dominate. Typical tools are Lyapunov exponents, strange attractors, symbolic dynamics and invariant measures, and a standard mathematical definition of a chaotic map is Devaney chaos. Classical examples are the Lorenz system in meteorology and the logistic map in population dynamics.