This analysis reveals how barcode entropy bounds metric entropy in pseudo-chord measures, suggesting deeper insights into Lagrangian geometry.
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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Çınelı et al. (2025) studied this question.
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