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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.25965 |
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| _version_ | 1866913161644343296 |
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| author | Cineli, Erman Ginzburg, Viktor L. Gurel, Basak Z. Mazzucchelli, Marco |
| author_facet | Cineli, Erman Ginzburg, Viktor L. Gurel, Basak Z. Mazzucchelli, Marco |
| contents | Barcode entropy is an invariant of a Hamiltonian system -- a Hamiltonian diffeomorphism or a Reeb flow -- measuring its Morse or Floer theoretic complexity at a small scale. More specifically, it is the exponential growth rate of the number of not-too-short bars in the Floer or symplectic homology persistence module. Barcode entropy is closely related to topological entropy, even though they originate in different contexts, and in low dimensions they coincide. In these notes, we study barcode entropy and related invariants in various settings and explore their connections with pure dynamics features and, in particular, topological entropy. The methods build on techniques from symplectic topology and Floer theory, dynamical systems, and smooth integral geometry. We also touch upon some other applications of the machinery we develop. These notes are based on the mini-course given by the second author at the CIME summer school "Symplectic Dynamics and Topology" (Cetraro, Italy, June 16-20, 2025). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25965 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topics in Symplectic Dynamics: Barcode Entropy Cineli, Erman Ginzburg, Viktor L. Gurel, Basak Z. Mazzucchelli, Marco Symplectic Geometry Dynamical Systems 53D40, 37B40, 37J12, 37J55 Barcode entropy is an invariant of a Hamiltonian system -- a Hamiltonian diffeomorphism or a Reeb flow -- measuring its Morse or Floer theoretic complexity at a small scale. More specifically, it is the exponential growth rate of the number of not-too-short bars in the Floer or symplectic homology persistence module. Barcode entropy is closely related to topological entropy, even though they originate in different contexts, and in low dimensions they coincide. In these notes, we study barcode entropy and related invariants in various settings and explore their connections with pure dynamics features and, in particular, topological entropy. The methods build on techniques from symplectic topology and Floer theory, dynamical systems, and smooth integral geometry. We also touch upon some other applications of the machinery we develop. These notes are based on the mini-course given by the second author at the CIME summer school "Symplectic Dynamics and Topology" (Cetraro, Italy, June 16-20, 2025). |
| title | Topics in Symplectic Dynamics: Barcode Entropy |
| topic | Symplectic Geometry Dynamical Systems 53D40, 37B40, 37J12, 37J55 |
| url | https://arxiv.org/abs/2605.25965 |