{
  "id": "2011.05641",
  "version": "v1",
  "published": "2020-11-11T09:09:19.000Z",
  "updated": "2020-11-11T09:09:19.000Z",
  "title": "On $C^0$-genericity of distributional chaos",
  "authors": [
    "Noriaki Kawaguchi"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $M$ be a compact smooth manifold without boundary. Based on results by Good and Meddaugh (2020), we prove that a strong distributional chaos is $C^0$-generic in the space of continuous self-maps (resp. homeomorphisms) of $M$. The results contain answers to questions by Li et al. (2016) and Moothathu (2011) in the zero-dimensional case. A related counter-example on the chain components under shadowing is also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-11T09:09:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "genericity",
      "compact smooth manifold",
      "strong distributional chaos",
      "results contain answers",
      "chain components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}