{
  "id": "1901.06589",
  "version": "v1",
  "published": "2019-01-19T21:42:28.000Z",
  "updated": "2019-01-19T21:42:28.000Z",
  "title": "Rendezvous with Sensitivity",
  "authors": [
    "Anima Nagar"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $(X,d)$ be a compact metric space and $f:X \\to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\\delta$ such that in each non-empty open subset there are distinct points whose iterates will be $\\delta-$apart at same instance. This dynamical property, though being a very weak one, brings in the essence of unpredictability in the system. In this article, we survey various sensitivities and some properties implied by and implying such sensitivities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-19T21:42:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "54H20"
    ],
    "keywords": [
      "sensitivity",
      "compact metric space",
      "non-empty open subset",
      "rendezvous",
      "distinct points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}