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Peer-reviewedCC BYJournal of fixed point theory and Its applications

From barcode entropy to metric entropy.

  • Erman Çineli1
  • Viktor L Ginzburg2
  • Başak Z Gürel3
  1. 1ETH Zürich, Rämistrasse 101, 8092 Zurich, Switzerland.
  2. 2Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064 USA.
  3. 3Department of Mathematics, University of Central Florida, Orlando, FL 32816 USA.
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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.

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Cite

BibTeXRIS
BibTeX
@article{cineli2026from,
  title = {{From barcode entropy to metric entropy.}},
  author = {Erman Çineli and Viktor L Ginzburg and Başak Z Gürel},
  journal = {Journal of fixed point theory and Its applications},
  year = {2026},
  month = may,
  doi = {10.1007/s11784-026-01301-y},
  url = {https://europepmc.org/article/MED/42927034},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - From barcode entropy to metric entropy.
AU  - Erman Çineli
AU  - Viktor L Ginzburg
AU  - Başak Z Gürel
PY  - 2026
DA  - 2026/05/26
JO  - Journal of fixed point theory and Its applications
DO  - 10.1007/s11784-026-01301-y
UR  - https://europepmc.org/article/MED/42927034
AB  - 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.
SN  - 1661-7738
SN  - 1661-7746
ER  -