The K-Property of Three Billiard Balls

Abstract

Sinai's strengthened version of the ergodic hypothesis is proved for three billiard balls on the v-dimensional torus: On connected components of the submanifold of the phase space specified by the trivial conservation laws of the energy and of the trajectory of the center of mass, the system is a K-flow. To cope with the difficulty that in the isomorphic one-particle-billiard system the scatterers are not strictly convex, geometric-algebraic, ergodic-theoretic and topological methods are elaborated