{
  "id": "0809.3941",
  "version": "v1",
  "published": "2008-09-23T15:26:57.000Z",
  "updated": "2008-09-23T15:26:57.000Z",
  "title": "A variational principle for topological pressure for certain non-compact sets",
  "authors": [
    "Daniel Thompson"
  ],
  "doi": "10.1112/jlms/jdp041",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $(X,d)$ be a compact metric space, $f:X \\mapsto X$ be a continuous map with the specification property, and $\\varphi: X \\mapsto \\IR$ be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form \\[ \\{x \\in X : \\lim_{n \\ra \\infty} \\frac{1}{n} \\sum_{i = 0}^{n-1} \\varphi (f^i (x)) = \\alpha \\}. \\] Analogous results were previously known for topological entropy. As an application, we prove multifractal analysis results for the entropy spectrum of a suspension flow over a continuous map with specification and the dimension spectrum of certain non-uniformly expanding interval maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-23T15:26:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45"
    ],
    "keywords": [
      "non-compact sets",
      "variational principle",
      "topological pressure",
      "compact metric space",
      "continuous map"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.3941T"
    }
  }
}