{
  "id": "2307.08126",
  "version": "v1",
  "published": "2023-07-16T19:00:04.000Z",
  "updated": "2023-07-16T19:00:04.000Z",
  "title": "Ergodicity of a surgered flow on unit tangent bundle of hyperbolic surface",
  "authors": [
    "Aritro Pathak"
  ],
  "categories": [
    "math.DS",
    "math.SG"
  ],
  "abstract": "Starting with a trivial periodic flow on $\\mathbb{S}M$, the unit tangent bundle of a genus two surface, we perform a Dehn-type surgery on the manifold around a tubular neighborhood of a curve on $\\mathbb{S}M$ that projects to a self-intersecting closed geodesic on $M$, to get a surgered flow which restricted to the surgery region is ergodic with respect to the volume measure. The surgered flow projects to a map on the surgery track that can be taken to be a linked twist map with oppositely oriented shears which generates the ergodic behavior for sufficiently strong shears in the surgery.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-16T19:00:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unit tangent bundle",
      "surgered flow",
      "hyperbolic surface",
      "ergodicity",
      "trivial periodic flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}