{
  "abstract": "For the Lozi map $L_{a,b}$, we consider parameter pairs for which the fixed point $X$ in the first quadrant has no homoclinic points and the period-two orbit $\\{P,P'\\}$ is attracting. For such parameters, let $\\ell$ denote the set of accumulation points of the unstable manifold $W_X^u$ that do not belong to $W_X^u$. We completely classify the forward asymptotic behavior of points in the phase space. The forward orbit of every point in the plane either converges to $X$, to the other fixed point $Y$ in the third quadrant, or to $\\ell$, or it escapes to infinity. The global phase space is organized by the stable manifolds of the fixed points: $W_Y^s$ separates the basin of $\\ell$ from the region of escaping orbits, while $W_X^s$ is the exceptional set of points whose orbits converge to $X$. In particular, if $\\mathcal{A}_1$ denotes the component of $\\mathbb{R}^2 \\setminus W_Y^s$ containing $X$, then $\\mathcal{A}_1 \\setminus W_X^s$ is precisely the basin of attraction of $\\ell$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11540",
  "author_total": 1,
  "authors": [
    {
      "name": "Kristijan Kilassa Kvaternik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9sm3scrngty8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11540",
  "fulltext_url": null,
  "id": "c9sm3scrngty8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11540",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7212249779",
  "pdf_url": "https://arxiv.org/pdf/2609.11540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9sm3scrngty8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11540"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Basins of attraction and escape in the Lozi map",
  "title_text": "Basins of attraction and escape in the Lozi map",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/c9sm3scrngty8",
  "venue": "arXiv",
  "versions": []
}