{
  "id": "1106.0150",
  "version": "v3",
  "published": "2011-06-01T12:00:46.000Z",
  "updated": "2013-06-20T03:03:17.000Z",
  "title": "Local Entropy Theory of a Random Dynamical System",
  "authors": [
    "Anthony H. Dooley",
    "Guohua Zhang"
  ],
  "comment": "All comments are welcome. Memoirs of the American Mathematical Society, to appear",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\\R$ or $\\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, we introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. We also discuss some variants of this variational principle. We introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply our variational principles to obtain a relationship between these of entropy tuples. Finally, we give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-20T03:03:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local entropy theory",
      "continuous bundle random dynamical system",
      "countable discrete amenable group",
      "variational principle",
      "entropy tuples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0150D"
    }
  }
}