Applying algorithmic complexity to define chaos in the motion of complex systems
A. Crisanti, M. Falcioni, Giorgio Mantica, Angelo Vulpiani · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1994
We define chaotic motion for dynamical systems acting in finite, discrete spaces via the deterministic randomness of their trajectories. The theory of algorithmic complexity is used to provide the meaning of randomness for symbolic sequences derived from these trajectories, and a practical test of randomness is devised on the basis of an ideal, physically motivated, model of a computer. Two examples---a discretized standard map, and a fully connected neutral network---are studied analytically and numerically.