{
  "id": "2001.06574",
  "version": "v1",
  "published": "2020-01-18T01:47:42.000Z",
  "updated": "2020-01-18T01:47:42.000Z",
  "title": "Unstable Entropy and Unstable Pressure for Partially Hyperbolic Endomorphisms",
  "authors": [
    "Xinsheng Wang",
    "Weisheng Wu",
    "Yujun Zhu"
  ],
  "comment": "25 pages. arXiv admin note: text overlap with arXiv:1811.12674",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, unstable metric entropy, unstable topological entropy and unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. A version of Shannon-McMillan-Breiman Theorem is established, and a variational principle is formulated, which gives a relationship between unstable metric entropy and unstable pressure (unstable topological entropy). As an application of the variational principle, some results on the $u$-equilibrium states are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-18T01:47:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35",
      "37B40",
      "37D30"
    ],
    "keywords": [
      "partially hyperbolic endomorphisms",
      "unstable pressure",
      "unstable entropy",
      "unstable metric entropy",
      "unstable topological entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}