3 research outputs found
Singularities and nonhyperbolic manifolds do not coincide
We consider the billiard flow of elastically colliding hard balls on the flat
-torus (), 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.Comment: Final version, to appear in Nonlinearit