{
  "id": "1307.8383",
  "version": "v3",
  "published": "2013-07-31T16:40:28.000Z",
  "updated": "2015-11-03T10:10:39.000Z",
  "title": "Confluence of singularities of non-linear differential equations via Borel--Laplace transformations",
  "authors": [
    "Martin Klimes"
  ],
  "comment": "42 pages",
  "journal": "Journal of Dynamical and Control Systems, 2015",
  "doi": "10.1007/s10883-015-9290-7",
  "categories": [
    "math.CA",
    "math.CV",
    "math.DS"
  ],
  "abstract": "Borel summable divergent series usually appear when studying solutions of analytic ODE near a multiple singular point. Their sum, uniquely defined in certain sectors of the complex plane, is obtained via the Borel--Laplace transformation. This article shows how to generalize the Borel--Laplace transformation in order to investigate bounded solutions of parameter dependent non-linear differential systems with two simple (regular) singular points unfolding a double (irregular) singularity. We construct parametric solutions on domains attached to both singularities, that converge locally uniformly to the sectoral Borel sums. Our approach provides a unified treatment for all values of the complex parameter.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-27T21:38:14.000Z",
      "title": "Confluence of singularities via Borel-Laplace transformations",
      "abstract": "This article shows how to generalize the Borel-Laplace transformation used in the summability theory of divergent series in order to investigate bounded solutions of parameter dependent nonlinear differential systems with two simple (regular) singular points unfolding a double (rank 1 irregular) singularity, that converge locally uniformly to the sectorial Borel sums. This method allows for a unified treatment in the spirit of resurgent analysis for all values of the parameter.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-11-03T10:10:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "borel-laplace transformation",
      "singularity",
      "parameter dependent nonlinear differential systems",
      "confluence",
      "sectorial borel sums"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.8383K"
    }
  }
}