{
  "abstract": "In this paper, we study the global injectivity of local diffeomorphisms in $\\mathbb{R}^n$, extending the criterions of Braun and Llibre in [{\\it Pacific J. Math.} {\\bf 333} (2024) 1--15] from the planar radial case to arbitrary dimension. Then we extend the results of Llibre and Mello in [{\\it Bull. Sci. Math.} {\\bf 213} (2026) 103889] to arbitrary dimension, obtaining two necessary and sufficient conditions for the real Jacobian conjecture in $\\mathbb{R}^n$ by qualitative theory of differential equations. Finally, using weighted Poincaré compactification in $\\mathbb{R}^n$, we provide a sufficient condition for the real Jacobian conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32391",
  "author_total": 3,
  "authors": [
    {
      "name": "Xinhao Hu"
    },
    {
      "name": "Jaume Llibre"
    },
    {
      "name": "Yilei Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7rmgs4s3zrz45.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32391",
  "fulltext_url": null,
  "id": "7rmgs4s3zrz45",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32391",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.32391",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7rmgs4s3zrz45.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32391",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32391"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Global injectivity and real Jacobian conjecture in $\\mathbb{R}^n$",
  "title_text": "Global injectivity and real Jacobian conjecture in ℝ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/7rmgs4s3zrz45",
  "venue": "arXiv",
  "versions": []
}