{
  "id": "2305.03910",
  "version": "v1",
  "published": "2023-05-06T03:16:50.000Z",
  "updated": "2023-05-06T03:16:50.000Z",
  "title": "Ergodic properties of multi-singular hyperbolic vector fields",
  "authors": [
    "Sylvain Crovisier",
    "Xiaodong Wang",
    "Dawei Yang",
    "Jinhua Zhang"
  ],
  "comment": "42 pages. Comments are welcome",
  "categories": [
    "math.DS"
  ],
  "abstract": "Bonatti and da Luz have introduced the class of multi-singular hyperbolic vector fields to characterize systems whose periodic orbits and singularities do not bifurcate under perturbation (called star vector fields). In this paper, we study the Sina\\\"{\\i}-Ruelle-Bowen measures for multi-singular hyperbolic vector fields: in a $C^1$ open and $C^1$ dense subset of multi-singular hyperbolic vector fields, each $C^\\infty$ one admits finitely many physical measures whose basins cover a full Lebesgue measure subset of the manifold. Similar results are also obtained for $C^1$ generic multi-singular hyperbolic vector fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-06T03:16:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ergodic properties",
      "generic multi-singular hyperbolic vector fields",
      "full lebesgue measure subset",
      "star vector fields",
      "dense subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}