From Barcode Entropy to Metric Entropy
Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel

TL;DR
This paper links barcode entropy with metric entropy, showing that barcode entropy provides a lower bound for metric entropy in certain invariant measures, refining previous bounds via the variational principle.
Contribution
It introduces pseudo-chord measures and establishes a lower bound of metric entropy by barcode entropy, refining the relationship between these entropies.
Findings
Barcode entropy bounds metric entropy from below.
The inequality refines the upper bound of barcode entropy by topological entropy.
Introduction of pseudo-chord measures for invariant measures.
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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Taxonomy
TopicsMathematical Dynamics and Fractals · Statistical Mechanics and Entropy · Quantum chaos and dynamical systems
