{
  "id": "math/0405467",
  "version": "v2",
  "published": "2004-05-24T19:45:38.000Z",
  "updated": "2005-10-14T17:59:13.000Z",
  "title": "Dimension groups for interval maps II: the transitive case",
  "authors": [
    "Fred Shultz"
  ],
  "comment": "32 pages, 1 postscript (eps) figure, LateX. minor changes. Has been accepted for publication in Ergodic Theory and Dynamical Systems",
  "categories": [
    "math.DS",
    "math.OA"
  ],
  "abstract": "Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially injective, the associated dimension group is a direct sum of simple dimension groups, each with a unique state.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-14T17:59:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "46L80"
    ],
    "keywords": [
      "interval maps",
      "transitive case",
      "transitive piecewise monotonic map",
      "dimension module",
      "simple dimension groups"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5467S"
    }
  }
}