{
  "id": "2004.05781",
  "version": "v1",
  "published": "2020-04-13T06:11:24.000Z",
  "updated": "2020-04-13T06:11:24.000Z",
  "title": "On Absolutely Continuous Invariant Measures and Krieger-Types of Markov Subshifts",
  "authors": [
    "Nachi Avraham-Re'em"
  ],
  "comment": "42 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "It is shown that for a non-singular conservative shift on a topologically-mixing Markov subshift with $\\textit{Doeblin Condition}$, the only possible absolutely continuous shift-invariant measure is a homogeneous Markov measure. Moreover, if it is not equivalent to a homogeneous Markov measure then the shift is of Krieger-type $\\mathrm{III}_1$. A criterion for equivalence of Markov measures is included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-13T06:11:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A20",
      "37A40",
      "60J10"
    ],
    "keywords": [
      "absolutely continuous invariant measures",
      "krieger-type",
      "homogeneous markov measure",
      "topologically-mixing markov subshift",
      "absolutely continuous shift-invariant measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}