{
  "id": "2312.00217",
  "version": "v1",
  "published": "2023-11-30T21:56:17.000Z",
  "updated": "2023-11-30T21:56:17.000Z",
  "title": "Topological equivalence in the infinity of a planar vector field and its principal part defined through Newton polytope",
  "authors": [
    "Thais Maria Dalbelo",
    "Regilene Oliveira",
    "Otavio Henrique Perez"
  ],
  "comment": "29 pages, 11 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a planar polynomial vector field $X$ with a fixed Newton polytope $\\mathcal{P}$, we prove (under some non degeneracy conditions) that the monomials associated to the upper boundary of $\\mathcal{P}$ determine (under topological equivalence) the phase portrait of $X$ in a neighbourhood of boundary of the Poincar\\'e--Lyapunov disk. This result can be seen as a version of the well known result of Berezovskaya, Brunella and Miari for the dynamics at the infinity, We also discuss the effect of the Poincar\\'e--Lyapunov compactification on the Newton polytope.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-30T21:56:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A26",
      "34C08"
    ],
    "keywords": [
      "planar vector field",
      "topological equivalence",
      "principal part",
      "planar polynomial vector field",
      "non degeneracy conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}