Singularities and non-hyperbolic manifolds do not coincide

Academic Article


  • We consider the billiard flow of elastically colliding hard balls on the flat v-torus (v ≥ 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. © 2013 IOP Publishing Ltd & London Mathematical Society.
  • Authors

    Published In

  • Nonlinearity  Journal
  • Digital Object Identifier (doi)

    Author List

  • Simányi N
  • Start Page

  • 1703
  • End Page

  • 1717
  • Volume

  • 26
  • Issue

  • 6