{
  "id": "1706.04212",
  "version": "v1",
  "published": "2017-06-13T18:14:03.000Z",
  "updated": "2017-06-13T18:14:03.000Z",
  "title": "Invariant measures for Fillipov systems",
  "authors": [
    "Douglas Duarte Novaes",
    "Régis Varão"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We are interested in Filippov systems which preserve a probability measure on a compact manifold. Using the formalism coming from the theory of differential inclusions, we define a measure to be invariant for a Filippov system as the natural analogous definition of invariant measure for flows. Our first main result states that if a differential inclusion admits an invariant probability measure, this measure does not see the trajectories where there is a break of uniqueness. Our second main result provides a necessary and sufficient condition in order to exist an invariant probability measure preserved by a Filippov system. Our third main result concerns Filippov systems which preserve a probability measure equivalent to the volume measure. As a corollary the volume preserving Filippov systems are the refractive ones. Then, in light of our previous results, we analyze the existence of invariant measures for many examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-13T18:14:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A36",
      "34A60",
      "37L40",
      "34C28"
    ],
    "keywords": [
      "invariant measure",
      "fillipov systems",
      "invariant probability measure",
      "main result concerns filippov systems",
      "third main result concerns filippov"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}