{
  "id": "2107.03493",
  "version": "v1",
  "published": "2021-07-07T21:40:53.000Z",
  "updated": "2021-07-07T21:40:53.000Z",
  "title": "Geometric Structure and Ergodic Properties of Bony Multi-Graphs",
  "authors": [
    "M. Rabiee",
    "F. H. Ghane",
    "M. Zaj"
  ],
  "comment": "23 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "The main goal in this paper is to describe the geometric structure of invariant graphs of a certain class of skew products. Our focus is on attracting multi-graphs. An invariant multi-graph is an invariant compact set which is a finite union of invariant graphs, and thus consists of a finite number of points on each fiber. We introduce invariant bony multi-graphs and construct an open set of skew products over an invertible base map (solenoid map) having attracting invariant multi-graphs and bony multi-graphs which support finitely many ergodic SRB measures. In this study some thermodynamic properties are investigated. Finally, we extend our results to a family of skew products over a generalized baker map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-07T21:40:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D35",
      "37C40",
      "37C70",
      "37H12"
    ],
    "keywords": [
      "geometric structure",
      "ergodic properties",
      "skew products",
      "invariant graphs",
      "invariant bony multi-graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}