{
  "id": "1205.0061",
  "version": "v5",
  "published": "2012-05-01T00:37:59.000Z",
  "updated": "2013-04-25T00:53:04.000Z",
  "title": "Singularities and nonhyperbolic manifolds do not coincide",
  "authors": [
    "Nandor Simanyi"
  ],
  "comment": "Final version, to appear in Nonlinearity",
  "journal": "Nonlinearity 26 (2013) 1703-1717",
  "doi": "10.1088/0951-7715/26/6/1703",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-04-25T00:53:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D50",
      "34D05"
    ],
    "keywords": [
      "nonhyperbolic manifolds",
      "boltzmann-sinai ergodic hypothesis",
      "elastically colliding hard balls",
      "billiard flow",
      "singularity manifold"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2013,
      "month": "Jun",
      "volume": 26,
      "number": 6,
      "pages": 1703
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013Nonli..26.1703S"
    }
  }
}