{
  "abstract": "In this paper, we study $r$-neutralized Pfister--Sullivan entropy, defined by measuring the complexity of orbit segments whose empirical measures lie near a prescribed invariant measure. We mainly obtain the following three results: (i) We disprove a variational conjecture posed by C.~Dong and Q.~Qiao [On $r$-neutralized entropy: entropy formula and existence of measures attaining the supremum, Comm. Math. Phys. 406 (2025), Article No. 74.] (ii)] We obtain variational formulas over probability measures for both upper and lower $r$-neutralized topological entropies. We also introduce new measure-theoretic quantities through PS localization and establish some variational principles for upper $r$-neutralized topological entropy (iii) We obtain upper bounds for $r$-neutralized PS entropy under different smoothness assumptions and lower bounds for $C^{1+α}$ diffeomorphisms, in terms of entropy, dimension and Lyapunov exponents. For $C^\\infty$ diffeomorphisms and $C^{1}$ Anosov diffeomorphisms, the $r$-neutralized PS entropies equal $h_μ(f)+r\\dim M$ for every ergodic measure $μ$. We also establish exact formulas on mixing surface hyperbolic basic sets and show that the whole-manifold measure formula can fail for $C^2$ surface diffeomorphisms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11639",
  "author_total": 3,
  "authors": [
    {
      "name": "Ercai Chen"
    },
    {
      "name": "Yunxiang Xie"
    },
    {
      "name": "Xiaoyao Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eb5wm518af5d3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11639",
  "fulltext_url": null,
  "id": "eb5wm518af5d3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11639",
  "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|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221180919",
  "pdf_url": "https://arxiv.org/pdf/2610.11639",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eb5wm518af5d3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11639",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11639"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Variational Principles for $r$-Neutralized Pfister-Sullivan Entropy",
  "title_text": "Variational Principles for r-Neutralized Pfister-Sullivan Entropy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/eb5wm518af5d3",
  "venue": "arXiv",
  "versions": []
}