{
  "id": "0804.2551",
  "version": "v1",
  "published": "2008-04-16T15:02:16.000Z",
  "updated": "2008-04-16T15:02:16.000Z",
  "title": "On the asymptotic measure of periodic subsystems of finite type in symbolic dynamics",
  "authors": [
    "J. -R. Chazottes",
    "Z. Coelho",
    "P. Collet"
  ],
  "comment": "Companion of the paper \"Poisson processes for subsystems of finite type in symbolic dynamics\"",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "Let $\\Delta\\subsetneq\\V$ be a proper subset of the vertices $\\V$ of the defining graph of an aperiodic shift of finite type $(\\Sigma_{A}^{+},\\S)$. Let $\\Delta_{n}$ be the union of cylinders in $\\Sigma_{A}^{+}$ corresponding to the points $x$ for which the first $n$-symbols of $x$ belong to $\\Delta$ and let $\\mu$ be an equilibrium state of a H\\\"older potential $\\phi$ on $\\Sigma_{A}^{+}$. We know that $\\mu(\\Delta_{n})$ converges to zero as $n$ diverges. We study the asymptotic behaviour of $\\mu(\\Delta_{n})$ and compare it with the pressure of the restriction of $\\phi$ to $\\Sigma_{\\Delta}$. The present paper extends some results in \\cite{CCC} to the case when $\\Sigma_{\\Delta}$ is irreducible and periodic. We show an explicit example where the asymptotic behaviour differs from the aperiodic case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-16T15:02:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35"
    ],
    "keywords": [
      "finite type",
      "asymptotic measure",
      "periodic subsystems",
      "symbolic dynamics",
      "asymptotic behaviour differs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.2551C"
    }
  }
}