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arXiv · 2507.13215

From Barcode Entropy to Metric Entropy

Erman Cineli·Viktor L. Ginzburg·Basak Z. Gurel
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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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Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel. 2025-07-17. From Barcode Entropy to Metric Entropy. https://arxiv.org/abs/2507.13215

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