{
  "abstract": "Fix a strip width \\(ρ>0\\), a Diophantine frequency \\(α\\), an integer \\(N\\ge2\\), and \\(λ>1\\). For the family \\[ V_{\\varepsilon,δ}(x) =2λ\\cos(2πN x)+\\varepsilonδ(x), \\] we prove that there is an open prevalent set \\(\\mathcal P_{\\rm strat}\\) of real-analytic strip-\\(ρ\\) perturbations such that every \\(δ\\in\\mathcal P_{\\rm strat}\\) admits \\(\\varepsilon_0(δ)>0\\) for which \\[ \\begin{gathered} \\operatorname{Leb}\\left\\{ E\\inΣ(V_{\\varepsilon,δ},α): ω(α,E;V_{\\varepsilon,δ})=s \\right\\}>0, 0<\\varepsilon<\\varepsilon_0(δ), \\qquad s=1,\\ldots,N. \\end{gathered} \\] The proof relates acceleration to the total multiplicity of real zeros of analytic overlap coefficients for first-return cocycles. Under quantitative control of the return products, Poisson integration and Kac normalization identify acceleration with half this multiplicity. A positive analytic dual state gives the finite-volume spectral gaps and Schur curvature needed at the upper spectral edge. Schur variations separate the perturbed maxima, and parameter exclusion preserves \\(s\\) pairs of simple zeros on a positive-measure spectral set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05243",
  "author_total": 3,
  "authors": [
    {
      "name": "Jinhao Liang"
    },
    {
      "name": "Yiqian Wang"
    },
    {
      "name": "Jiahao Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rk4hap5ycnbm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05243",
  "fulltext_url": null,
  "id": "8rk4hap5ycnbm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05243",
  "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",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7220720599",
  "pdf_url": "https://arxiv.org/pdf/2610.05243",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rk4hap5ycnbm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05243",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05243"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Positive-Measure Acceleration Strata for Prevalent Perturbations of N-Fold Pullbacks of Supercritical Almost Mathieu Potentials",
  "title_text": "Positive-Measure Acceleration Strata for Prevalent Perturbations of N-Fold Pullbacks of Supercritical Almost Mathieu Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8rk4hap5ycnbm",
  "venue": "arXiv",
  "versions": []
}