{
  "id": "2309.09154",
  "version": "v1",
  "published": "2023-09-17T04:38:56.000Z",
  "updated": "2023-09-17T04:38:56.000Z",
  "title": "Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors",
  "authors": [
    "A. E. Calderón",
    "E. Villar-Sepúlveda"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the attractor $\\Lambda$ of a piecewise contracting map $f$ defined on a compact interval. If $f$ is injective, we show that it is possible to estimate the topological entropy of $f$ (according to Bowen's formula) and the Hausdorff dimension of $\\Lambda$ via the complexity associated with the orbits of the system. Specifically, we prove that both numbers are zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-17T04:38:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise contracting map",
      "hausdorff dimension",
      "compact interval",
      "bowens formula",
      "topological entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}