{
  "id": "2406.16579",
  "version": "v1",
  "published": "2024-06-24T12:15:05.000Z",
  "updated": "2024-06-24T12:15:05.000Z",
  "title": "Note on the metric entropy for multivalued maps",
  "authors": [
    "Jan Andres",
    "Pavel Ludvík"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "The main aim of this note is to point out by means of counter-examples that some arguments of the proofs of two theorems about a \"half variational principle\" for multivalued maps, formulated recently by Vivas and Sirvent [Metric entropy for set-valued maps, Discrete Contin. Dyn. Syst. Ser. B, 27 (2022), pp. 6589-6604], are false and that our corrected versions require rather restrictive additional assumptions. Nevertheless, we will be able to establish the full variational principle for a special subclass of multivalued lower semicontinuous maps with convex compact values on a compact subset of a Banach space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-24T12:15:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28D20",
      "37B40",
      "54C60"
    ],
    "keywords": [
      "metric entropy",
      "multivalued maps",
      "half variational principle",
      "full variational principle",
      "convex compact values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}