{
  "id": "1707.07156",
  "version": "v1",
  "published": "2017-07-22T12:53:14.000Z",
  "updated": "2017-07-22T12:53:14.000Z",
  "title": "Degree counting for Toda system with simple singularity : one point blow up",
  "authors": [
    "Youngae Lee",
    "Chang-shou Lin",
    "Wen Yang",
    "Lei Zhang"
  ],
  "comment": "31 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the degree counting formula of the rank two Toda system with simple singular source when $\\rho_1\\in(0,4\\pi)\\cup(4\\pi,8\\pi)$ and $\\rho_2\\notin 4\\pi\\mathbb{N}.$ The key step is to derive the degree formula of the shadow system, which arises from the bubbling solutions as $\\rho_1$ tends to $4\\pi$. In order to compute the topological degree of the shadow system, we need to find some suitable deformation. During this deformation, we shall deal with \\textit{new} difficulty arising from the new phenomena: blow up does not necessarily imply concentration of mass. This phenomena occurs due to the collapsing of singularities. This is a continuation of the previous work Lee, Lin, Wei and Yang.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-22T12:53:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J47",
      "58J05"
    ],
    "keywords": [
      "toda system",
      "point blow",
      "simple singularity",
      "shadow system",
      "simple singular source"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}