From Barcode Entropy to Metric Entropy
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916849163173888 |
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| author | Cineli, Erman Ginzburg, Viktor L. Gurel, Basak Z. |
| author_facet | Cineli, Erman Ginzburg, Viktor L. Gurel, Basak Z. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_13215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Barcode Entropy to Metric Entropy Cineli, Erman Ginzburg, Viktor L. Gurel, Basak Z. Symplectic Geometry Dynamical Systems 53D40, 37C40, 37J12, 37J46, 37J55 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. |
| title | From Barcode Entropy to Metric Entropy |
| topic | Symplectic Geometry Dynamical Systems 53D40, 37C40, 37J12, 37J46, 37J55 |
| url | https://arxiv.org/abs/2507.13215 |