{
  "id": "2410.11117",
  "version": "v1",
  "published": "2024-10-14T22:01:33.000Z",
  "updated": "2024-10-14T22:01:33.000Z",
  "title": "Weak mixing in rational billiards",
  "authors": [
    "Francisco Arana-Herrera",
    "Jon Chaika",
    "Giovanni Forni"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin, modulo some low complexity exceptions. This proves a longstanding conjecture of Gutkin. This result is derived from a complete characterization of translation surfaces that are weakly mixing in almost every direction: they are those that do not admit an affine factor map to the circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-14T22:01:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25",
      "37C83",
      "37E35",
      "37F34"
    ],
    "keywords": [
      "rational billiards",
      "weak mixing",
      "low complexity exceptions",
      "affine factor map",
      "characterize rational polygons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}