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<p>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 <i>pseudo-chord measures</i>. This inequality refines, via the variational principle, the previously known upper bound of barcode entropy by topological entropy.</p>

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From barcode entropy to metric entropy

  • 期刊论文

  • 发表日期：

    2026年5月26日

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  • Erman Çineli,
  • Viktor L. Ginzburg,
  • Başak Z. Gürel

摘要

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.