{
  "id": "2407.16650",
  "version": "v1",
  "published": "2024-07-23T17:05:14.000Z",
  "updated": "2024-07-23T17:05:14.000Z",
  "title": "Anosov diffeomorphisms of open surfaces",
  "authors": [
    "Snir Ben Ovadia",
    "Jonathan DeWitt"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the existence of Anosov diffeomorphisms on complete open surfaces. We show that under the assumptions of density of periodic points and uniform geometry that such diffeomorphisms have a system of Margulis measures, which are a holonomy invariant and dynamically invariant system of measures along the stable and unstable leaves. This shows that there can be no such diffeomorphism with a global product structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-23T17:05:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anosov diffeomorphisms",
      "global product structure",
      "complete open surfaces",
      "dynamically invariant system",
      "periodic points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}