{
  "id": "1805.05692",
  "version": "v1",
  "published": "2018-05-15T10:34:32.000Z",
  "updated": "2018-05-15T10:34:32.000Z",
  "title": "A Central Limit Theorem for Periodic Orbits of Hyperbolic Flows",
  "authors": [
    "Stephen Cantrell",
    "Richard Sharp"
  ],
  "comment": "9 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a counting problem in the setting of hyperbolic dynamics. Let $\\phi_t : \\Lambda \\to \\Lambda$ be a weak mixing hyperbolic flow. We count the proportion of prime periodic orbits of $\\phi_t$, with length less than $T$, that satisfy an averaging condition related to a H\\\"older continuous function $f: \\Lambda \\to \\mathbb{R}$. We show, assuming an approximability condition on $\\phi$ (or unconditionally when $\\phi$ is a transitive Anosov flow), that as $T \\to \\infty$, we obtain a central limit theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-15T10:34:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "prime periodic orbits",
      "weak mixing hyperbolic flow",
      "transitive anosov flow",
      "hyperbolic dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}