{
  "id": "1106.0111",
  "version": "v1",
  "published": "2011-06-01T07:51:22.000Z",
  "updated": "2011-06-01T07:51:22.000Z",
  "title": "The topological entropy of Banach spaces",
  "authors": [
    "Jozef Bobok",
    "Henk Bruin"
  ],
  "comment": "The paper is going to appear at Journal of Difference Equations and Applications",
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate some properties of (universal) Banach spaces of real functions in the context of topological entropy. Among other things, we show that any subspace of $C([0,1])$ which is isometrically isomorphic to $\\ell_1$ contains a functions with infinite topological entropy. Also, for any $t \\in [0, \\infty]$, we construct a (one-dimensional) Banach space in which any nonzero function has topological entropy equal to $t$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-01T07:51:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach space",
      "infinite topological entropy",
      "real functions",
      "nonzero function",
      "topological entropy equal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0111B"
    }
  }
}