{
  "id": "1502.06179",
  "version": "v1",
  "published": "2015-02-22T05:17:35.000Z",
  "updated": "2015-02-22T05:17:35.000Z",
  "title": "Cherry flow: physical measures and perturbation theory",
  "authors": [
    "Jiagang Yang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this article we consider Cherry flows on torus which have two singularities: a source and a saddle, and no periodic orbits. We show that every Cherry flow admits a unique physical measure, whose basin has full volume. This proves a conjecture given by R. Saghin and E. Vargas in~\\cite{SV}. We also show that the perturbation of Cherry flow depends on the divergence at the saddle: when the divergence is negative, this flow admits a neighborhood, such that any flow in this neighborhood belongs to the following three cases: (a) has a saddle connection; (b) a Cherry flow; (c) a Morse-Smale flow whose non-wandering set consists two singularities and one periodic sink. In contrary, when the divergence is non-negative, this flow can be approximated by non-hyperbolic flow with arbitrarily larger number of periodic sinks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-22T05:17:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A99",
      "37D25",
      "37E35"
    ],
    "keywords": [
      "perturbation theory",
      "periodic sink",
      "cherry flow admits",
      "cherry flow depends",
      "divergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150206179Y"
    }
  }
}