From Barcode Entropy to Metric Entropy
Symplectic Geometry
2025-07-18 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2507.13215,
title = {From Barcode Entropy to Metric Entropy},
author = {Erman Cineli and Viktor L. Ginzburg and Basak Z. Gurel},
journal= {arXiv preprint arXiv:2507.13215},
year = {2025}
}
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18 pages