THE BILLIARD ALGORITHM AND KS ENTROPY

There is known to be a close relation between the Kolmogorov-Sinai entropy (sum of the positive Lyapunov exponents) of an ergodic dynamical system and the algorithmic complexity of encoding trajectories of the system with respect to some partition. In this letter, we explicitly give an encoding which demonstrates this relation for the square Sinai billiard. The encoding depends on the fact that the collision criterion for the billiard is an example of rational approximants. The method may be used to achieve very fast simulation times for the system.