{
  "id": "1811.04034",
  "version": "v1",
  "published": "2018-11-09T17:36:55.000Z",
  "updated": "2018-11-09T17:36:55.000Z",
  "title": "Dynamics on Hyperspaces",
  "authors": [
    "Victor Ayala",
    "Adriano Da Silva",
    "Heriberto Roman-Flores"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a compact metric space (X; \\varrho) and a continuous function f:X\\rightarrow X, we study the dynamics of the induced map \\bar{f} on the hyperspace of the compact subsets of X. We show how the chain recurrent set of f and its components are related with the one of the induced map. The main result of the paper proves that, under mild conditions, the numbers of chain components of \\bar{f} is greater than the ones of f. Showing the richness in the dynamics of \\bar{f} which cannot be perceived by f.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-09T17:36:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperspace",
      "compact metric space",
      "induced map",
      "chain recurrent set",
      "mild conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}