Singularities and nonhyperbolic manifolds do not coincide

摘要: We consider the billiard flow of elastically colliding hard balls on flat $\nu$-torus ($\nu\ge 2$), and prove that no singularity manifold can even locally coincide with a describing future non-hyperbolicity trajectories. As corollary, we obtain ergodicity (actually Bernoulli mixing property) all such systems, i.e. verification Boltzmann-Sinai Ergodic Hypothesis.