{
  "id": "1909.07317",
  "version": "v1",
  "published": "2019-09-16T16:25:48.000Z",
  "updated": "2019-09-16T16:25:48.000Z",
  "title": "Measures of maximal entropy on subsystems of topological suspension semi-flows",
  "authors": [
    "Tamara Kucherenko",
    "Daniel J. Thompson"
  ],
  "comment": "v1: 10 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a compact topological dynamical system (X, f) with positive entropy and upper semi-continuous entropy map, and any closed invariant subset $Y \\subset X$ with positive entropy, we show that there exists a continuous roof function such that the set of measures of maximal entropy for the suspension semi-flow over (X,f) consists precisely of the lifts of measures which maximize entropy on Y. This result has a number of implications for the possible size of the set of measures of maximal entropy for topological suspension flows. In particular, for a suspension flow on the full shift on a finite alphabet, the set of ergodic measures of maximal entropy may be countable, uncountable, or have any finite cardinality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-16T16:25:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "37A35"
    ],
    "keywords": [
      "maximal entropy",
      "topological suspension semi-flows",
      "subsystems",
      "upper semi-continuous entropy map",
      "positive entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}