{
  "abstract": "Let $Γ<\\mathsf{SL}(d,\\mathbb R)$ be a torsion-free, Zariski-dense Borel-Anosov subgroup, and let $φ$ be a linear functional positive on the limit cone of $Γ$. For every $χ\\in \\operatorname{Hom}(Γ, \\mathbb R)$, we construct twisted $(φ,χ)$-conformal densities and prove their existence, uniqueness and ergodicity. For every non-trivial normal subgroup $Γ_0\\lhdΓ$ with nilpotent quotient, we classify the ergodic $φ$-conformal densities of $Γ_0$ in terms of characters of $Γ/Γ_0$. Up to scaling, they are naturally parametrized by $\\operatorname{Hom}(Γ/Γ_0,\\mathbb R)$, and their dimensions are precisely the critical exponents of the corresponding twisted Poincaré series. We also prove a shadow lemma for twisted densities of normal subgroups, with estimates uniform over densities with fixed parameters, and a twisted Hopf-Tsuji-Sullivan theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27125",
  "author_total": 2,
  "authors": [
    {
      "name": "Krishnendu Gongopadhyay"
    },
    {
      "name": "Neelanjan Mondal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/083esfbszffrd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27125",
  "fulltext_url": null,
  "id": "083esfbszffrd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27125",
  "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"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214187062",
  "pdf_url": "https://arxiv.org/pdf/2609.27125",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/083esfbszffrd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.27125",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27125"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Twisted Patterson-Sullivan densities on nilpotent covers for Anosov subgroups",
  "title_text": "Twisted Patterson-Sullivan densities on nilpotent covers for Anosov subgroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/083esfbszffrd",
  "venue": "arXiv",
  "versions": []
}