{
  "id": "1308.2810",
  "version": "v1",
  "published": "2013-08-13T10:23:01.000Z",
  "updated": "2013-08-13T10:23:01.000Z",
  "title": "Chaos in Topological Spaces",
  "authors": [
    "John Taylor"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform Hausdorff space, there is a meaningful definition of sensitive dependence on initial conditions, and prove that if a map is chaotic on a such a space, then it necessarily has sensitive dependence on initial conditions. The proof is interesting in that it explains very clearly what causes a chaotic process to have sensitive dependence. Finally, we construct a chaotic map on a non-metrizable topological space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-13T10:23:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sensitive dependence",
      "initial conditions",
      "uniform hausdorff space",
      "devanney definition",
      "topological space happens"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.2810T"
    }
  }
}