Georgia Institute of Technology College of Sciences

Putting in place the last piece of the big mosaic of the proof of the Boltzmann-Sinai Ergodic Hypothesis,we consider the billiard flow of elastically colliding hard balls on the flat $d$-torus ($d>1$), 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. The manuscript of the paper can be found at http://people.cas.uab.edu/~simanyi/transversality-new.pdf