Numerical experiments on the free motion of a point mass moving in a plane convex region: Stochastic transition and entropy

Abstract

We numerically investigate the behavior of a simple dynamical system, a plane billiard which by a continuous deformation of the border passes from a completely integrable system to a well-defined type of completely stochastic system, namely a $K$ system. A stochastic transition is observed, with the usual coexistence of ordered and stochastic regions. Moreover, the stochastic region at certain intermediate stages appears to be separated into several invariant components. An estimate of the Kolmogorov entropy is presented.