{
  "id": "1903.07635",
  "version": "v1",
  "published": "2019-03-18T18:00:59.000Z",
  "updated": "2019-03-18T18:00:59.000Z",
  "title": "Counting closed geodesics in a compact rank one locally CAT(0) space",
  "authors": [
    "Russell Ricks"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Let $X$ be a compact, geodesically complete, locally CAT(0) space such that the universal cover admits a rank one axis. Assume $X$ is not homothetic to a metric graph with integer edge lengths. Let $P_t$ be the number of parallel classes of oriented closed geodesics of length $\\le t$; then $\\lim\\limits_{t \\to \\infty} P_t / \\frac{e^{ht}}{ht} = 1$, where $h$ is the entropy of the geodesic flow on the space $SX$ of parametrized unit-speed geodesics in $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-18T18:00:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "counting closed geodesics",
      "locally cat",
      "compact rank",
      "universal cover admits",
      "integer edge lengths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}