{
  "id": "0912.1783",
  "version": "v1",
  "published": "2009-12-09T16:15:04.000Z",
  "updated": "2009-12-09T16:15:04.000Z",
  "title": "Orders of accumulation of entropy on manifolds",
  "authors": [
    "Kevin McGoff"
  ],
  "comment": "36 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a continuous self-map $T$ of a compact metrizable space with finite topological entropy, the order of accumulation of entropy of $T$ is a countable ordinal that arises in the theory of entropy structure and symbolic extensions. Given any compact manifold $M$ and any countable ordinal $\\al$, we construct a continuous, surjective self-map of $M$ having order of accumulation of entropy $\\al$. If the dimension of $M$ is at least 2, then the map can be chosen to be a homeomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-09T16:15:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37B40"
    ],
    "keywords": [
      "accumulation",
      "countable ordinal",
      "finite topological entropy",
      "compact metrizable space",
      "entropy structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1783M"
    }
  }
}