{
  "id": "1901.07972",
  "version": "v1",
  "published": "2019-01-23T16:01:22.000Z",
  "updated": "2019-01-23T16:01:22.000Z",
  "title": "The space of invariant measures for countable Markov shifts",
  "authors": [
    "Godofredo Iommi",
    "Anibal Velozo"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov shifts, the space of invariant sub-probability measures is a Poulsen simplex and that its extreme points are the ergodic invariant probability measures together with the zero measure. In particular we obtain that the space of invariant probability measures is a Poulsen simplex minus a vertex and the corresponding convex combinations. Our results apply to finite entropy non-locally compact transitive countable Markov shifts and to every locally compact transitive countable Markov shift. In order to prove these results we introduce a topology on the space of measures that generalizes the vague topology to a class of non-locally compact spaces, the topology of convergence on cylinders. We also prove analogous results for suspension flows defined over countable Markov shifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-23T16:01:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariant probability measures",
      "invariant measures",
      "compact transitive countable markov shift",
      "poulsen simplex",
      "non-locally compact transitive"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}