{
  "abstract": "The goal of this paper is to generalize recent results about the topological classification of the dynamics of a real planar polynomial vector field near infinity. Given a polynomial vector field $X$, using Newton polyhedra one can define its generalized upper principal part $X_Γ^{U}$. By dropping some monomials of $X_Γ^{U}$, we define its minimal generalized upper principal part $X_{G}^{U}$. We prove that there exist an open and dense set $\\widetilde{\\mathfrak{U}}_{1}$ in the set of polynomial vector fields with Newton degenerate upper principal part satisfying the following property: if $X\\in\\widetilde{\\mathfrak{U}}_{1}$, then $X$ and $X_{G}^{U}$ are topologically equivalent near infinity, provided that $X_{G}^{U}$ satisfies some additional non-degeneracy assumptions. Our techniques rely on toric compactification and the Normal Form Theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04413",
  "author_total": 3,
  "authors": [
    {
      "name": "Thaís Maria Dalbelo"
    },
    {
      "name": "Regilene Oliveira"
    },
    {
      "name": "Otavio Henrique Perez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0cve5t09y9yfb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04413",
  "fulltext_url": null,
  "id": "0cve5t09y9yfb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04413",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7211900730",
  "pdf_url": "https://arxiv.org/pdf/2609.04413",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0cve5t09y9yfb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04413",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04413"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Generalized upper principal part of real planar polynomial vector fields",
  "title_text": "Generalized upper principal part of real planar polynomial vector fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/0cve5t09y9yfb",
  "venue": "arXiv",
  "versions": []
}