{
  "abstract": "We establish a connection between barcode entropy and metric entropy. Namely, we show that the barcode entropy bounds the metric entropy from below for a measure from a specific class of invariant measures associated with a pair of Lagrangian or Legendrian submanifolds, which we call pseudo-chord measures. This inequality refines, via the variational principle, the previously known upper bound of barcode entropy by topological entropy.",
  "abstract_shown": true,
  "affiliations": [
    "ETH Zürich, Rämistrasse 101, 8092 Zurich, Switzerland.",
    "Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064 USA.",
    "Department of Mathematics, University of Central Florida, Orlando, FL 32816 USA."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Erman Çineli"
    },
    {
      "affs": [
        1
      ],
      "name": "Viktor L Ginzburg"
    },
    {
      "affs": [
        2
      ],
      "name": "Başak Z Gürel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enrvpbdzkn2af.bib",
  "cited_by": 0,
  "doi": "10.1007/s11784-026-01301-y",
  "fulltext_url": "https://europepmc.org/articles/PMC13694310",
  "id": "enrvpbdzkn2af",
  "issns": [
    "1661-7738",
    "1661-7746"
  ],
  "landing_url": "https://europepmc.org/article/MED/42927034",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W4415310449",
  "pdf_url": "https://europepmc.org/articles/PMC13694310?pdf=render",
  "pmcid": "PMC13694310",
  "pmid": "42927034",
  "published": "2026-05-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enrvpbdzkn2af.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:20Z",
      "native_id": "MED:42927034",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42927034"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Mathematical Dynamics and Fractals",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "From barcode entropy to metric entropy.",
  "title_text": "From barcode entropy to metric entropy.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:21:20Z",
  "url": "https://research.draconitic.com/paper/enrvpbdzkn2af",
  "venue": "Journal of fixed point theory and Its applications",
  "versions": []
}