Singularities and non-hyperbolic manifolds do not coincide

We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann–Sinai ergodic hypothesis. Mathematics Subject Classification: 37D50, 34D05