{
  "id": "1209.2390",
  "version": "v2",
  "published": "2012-09-11T18:37:31.000Z",
  "updated": "2012-09-30T08:46:56.000Z",
  "title": "The Octagonal PET I: Renormalization and Hyperbolic Symmetry",
  "authors": [
    "Richard Evan Schwartz"
  ],
  "comment": "77 pages, mildly computer-assisted proof. The paper has a companion Java program, available to download from the author's website. This new version has a title change, to reflect the fact that there is now a sequel paper. A result from the sequel is mentioned. Several typos are fixed. 3 references are added",
  "categories": [
    "math.DS"
  ],
  "abstract": "We introduce a family of polytope exchange transformations (PETs) acting on parallelotopes in $\\R^{2n}$ for $n=1,2,3...$. These PETs are constructed using a pair of lattices in $\\R^{2n}$. The moduli space of these PETs is $GL_n(\\R)$. We study the case n=1 in detail. In this case, we show that the 2-dimensional family is completely renormalizable and that the $(2,4,\\infty)$ hyperbolic reflection triangle group acts (by linear fractional transformations) as the renormalization group on the moduli space. These results have a number of geometric corollaries for the system. Most of the paper is traditional mathematics, but some part of the paper relies on a rigorous computer-assisted proof involving integer calculations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-30T08:46:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic symmetry",
      "octagonal pet",
      "hyperbolic reflection triangle group acts",
      "renormalization",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 77,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2390S"
    }
  }
}