{
  "id": "math/0407368",
  "version": "v2",
  "published": "2004-07-22T03:27:47.000Z",
  "updated": "2010-08-11T07:37:21.000Z",
  "title": "The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions (Without Exceptional Models)",
  "authors": [
    "Nandor Simanyi"
  ],
  "comment": "Paper withdrawn due to a substantial error",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the system of $N$ ($\\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ in the flat unit torus $\\Bbb T^\\nu$, $\\nu\\ge2$. In the case $\\nu=2$ we prove (the full hyperbolicity and) the ergodicity of such systems for every selection $(m_1,...,m_N;r)$ of the external geometric parameters, without exceptional values. In higher dimensions, for hard ball systems in $\\Bbb T^\\nu$ ($\\nu\\ge3$), we prove that every such system (is fully hyperbolic and) has open ergodic components.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-11T07:37:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D50",
      "34D05"
    ],
    "keywords": [
      "boltzmann-sinai ergodic hypothesis",
      "exceptional models",
      "external geometric parameters",
      "flat unit torus",
      "hard ball systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}