{
  "id": "2404.18495",
  "version": "v1",
  "published": "2024-04-29T08:23:18.000Z",
  "updated": "2024-04-29T08:23:18.000Z",
  "title": "A Simple Example of Pathological Foliations in Skew-Product Diffeomorphisms",
  "authors": [
    "Zhihong Xia",
    "Peizheng Yu"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Inspired by examples of Katok and Milnor \\cite{Milnor1997}, we construct a simple example of skew-product volume preserving diffeomorphism where the center foliation is pathological in the sense that, there is a full measure set whose intersection with any center leaf contains at most one point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-29T08:23:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple example",
      "skew-product diffeomorphisms",
      "pathological foliations",
      "full measure set",
      "skew-product volume preserving diffeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}