Singularities and nonhyperbolic manifolds do not coincide

@article{Simnyi2012SingularitiesAN,
  title={Singularities and nonhyperbolic manifolds do not coincide},
  author={Nandor Sim{\'a}nyi},
  journal={arXiv: Dynamical Systems},
  year={2012}
}
  • N. Simányi
  • Published 1 May 2012
  • Mathematics, Physics
  • arXiv: Dynamical Systems
We consider the billiard flow of elastically colliding hard balls on the flat $\nu$-torus ($\nu\ge 2$), 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. 
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