{
  "id": "2407.11602",
  "version": "v1",
  "published": "2024-07-16T10:57:44.000Z",
  "updated": "2024-07-16T10:57:44.000Z",
  "title": "A Frobenius-type theory for discrete systems",
  "authors": [
    "Daniel Reyes",
    "Miguel A. Rodríguez",
    "Piergiulio Tempesta"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We develop an approach analogous to classical Frobenius theory for the analysis of singularities of ODEs in the case of discrete dynamical systems. Our methodology is based on the Roman-Rota theory of finite operators and relies crucially on the idea of preserving the Leibniz rule on a lattice of points by means of the notion of Rota algebras. The relevant cases of the Bessel, Hermite and Airy equations are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-16T10:57:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A05",
      "37J70"
    ],
    "keywords": [
      "discrete systems",
      "frobenius-type theory",
      "airy equations",
      "relevant cases",
      "classical frobenius theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}