{
  "id": "math/0605358",
  "version": "v6",
  "published": "2006-05-14T05:00:40.000Z",
  "updated": "2009-01-31T19:27:31.000Z",
  "title": "Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis",
  "authors": [
    "Nandor Simanyi"
  ],
  "comment": "Final version; to appear in Inventiones Mathematicae",
  "journal": "Inventiones Mathematicae, Vol. 177, No. 2 (2009), pp. 381-413",
  "doi": "10.1007/s00222-009-0182-x",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the system of $N$ ($\\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\\Bbb T^\\nu$, $\\nu\\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full hyperbolicity and ergodicity of such systems for every selection $(m_1,...,m_N;r)$ of the external geometric parameters, provided that almost every singular orbit is geometrically hyperbolic (sufficient), i. e. the so called Chernov-Sinai Ansatz is true. The present proof does not use the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools from geometric analysis.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2009-01-31T19:27:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D50",
      "34D05"
    ],
    "keywords": [
      "boltzmann-sinai ergodic hypothesis",
      "conditional proof",
      "flat unit torus",
      "external geometric parameters",
      "full hyperbolicity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5358S"
    }
  }
}