{
  "abstract": "In this paper, we show that for a shift dynamical system $(X_{\\mathcal{L}}, σ)$ with a weakened form of the specification property, there exists a Xiong chaotic set $C$ of $X_{\\mathcal{L}}$ with full topological entropy everywhere (i.e. the intersection of $C$ and arbitrary non-empty open subset of $X_{\\mathcal{L}}$ has full topological entropy). Moreover, $C$ satisfies that for any non-empty subset $A$ and any continuous map $F: A\\rightarrow X_{\\mathcal{L}},$ there exists an increasing sequence $\\{p_{k}\\}_{k=1}^{+\\infty}$ of positive integers such that $\\lim\\limits_{k\\rightarrow +\\infty}σ^{p_{k}}(x)=F(x)$ holds for any $x\\in A.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29171",
  "author_total": 1,
  "authors": [
    {
      "name": "Xinyun Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/an846v1dbqs53.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29171",
  "fulltext_url": null,
  "id": "an846v1dbqs53",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29171",
  "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": "W7204892522",
  "pdf_url": "https://arxiv.org/pdf/2608.29171",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/an846v1dbqs53.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.29171",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29171"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Full Topological entropy of Xiong chaotic sets beyond the specification property",
  "title_text": "Full Topological entropy of Xiong chaotic sets beyond the specification property",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/an846v1dbqs53",
  "venue": "arXiv",
  "versions": []
}