{
  "abstract": "We study the equality case of the inequalities between the Lyapunov spectrum and the Harder--Narasimhan slopes of a semi-simple local system with non-expanding cusp monodromy over a finite-area hyperbolic surface. This gives a nonlattice-transversality alternative of the monodromy group. On the other hand, we generalize Filip's Assumptions A and B to give classes of polarized variation of Hodge structures that achieve the equality. As an application, we recover the thinness of C-32 in $\\mathrm{Sp}_6\\mathbb{R}$. Besides, we provide an upper bound, called average Cartan spectrum, that dominates the Lyapunov spectrum and study its rigidity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06388",
  "author_total": 2,
  "authors": [
    {
      "name": "Fei Yu"
    },
    {
      "name": "Junming Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apky13eyhzwhc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06388",
  "fulltext_url": null,
  "id": "apky13eyhzwhc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06388",
  "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.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apky13eyhzwhc.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Lyapunov spectrum, Harder--Narasimhan filtration and thin monodromy",
  "title_text": "Lyapunov spectrum, Harder--Narasimhan filtration and thin monodromy",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/apky13eyhzwhc",
  "venue": "arXiv",
  "versions": []
}