{
  "abstract": "In this paper, we establish a new type of stability phenomenon for the topological entropy of Hamiltonian diffeomorphisms of closed surfaces. For a closed surface endowed with an area form $(Σ,ω)$ and a Hamiltonian diffeomorphism $ϕ$ of $(Σ,ω)$, we show that for every $\\varepsilon>0$ there exists $A=A(ϕ,\\varepsilon)>0$ such that \\[ h_{\\mathrm{top}}(ϕ') > h_{\\mathrm{top}}(ϕ)-\\varepsilon \\] for every Hamiltonian diffeomorphism $ϕ'$ obtained from $ϕ$ by a deformation supported in a disjoint union of disks, each of area less than $A$. In particular, if $h_{\\mathrm{top}}(ϕ)>0$, then $ϕ$ cannot be made to have zero entropy by an area-preserving deformation supported in disks of small area. This follows from the new braid stability result established in this paper with respect to the spectral distance recently introduced by Connery-Grigg.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.31132",
  "author_total": 3,
  "authors": [
    {
      "name": "Marcelo R. R. Alves"
    },
    {
      "name": "Matthias Meiwes"
    },
    {
      "name": "Beomjun Sohn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zq1hvm1z99ac.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.31132",
  "fulltext_url": null,
  "id": "9zq1hvm1z99ac",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.31132",
  "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.SG"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7204864734",
  "pdf_url": "https://arxiv.org/pdf/2608.31132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zq1hvm1z99ac.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.31132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.31132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Robustness of topological entropy under small area deformations",
  "title_text": "Robustness of topological entropy under small area deformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/9zq1hvm1z99ac",
  "venue": "arXiv",
  "versions": []
}