On the Barcode Entropy of Reeb Flows
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909924969152512 |
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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 | In this paper we continue investigating connections between Floer theory and dynamics of Hamiltonian systems, focusing on the barcode entropy of Reeb flows. Barcode entropy is the exponential growth rate of the number of not-too-short bars in the Floer or symplectic homology persistence module. The key novel result is that the barcode entropy is bounded from below by the topological entropy of any hyperbolic invariant set. This, combined with the fact that the topological entropy bounds the barcode entropy from above, established by Fender, Lee and Sohn, implies that in dimension three the two types of entropy agree. The main new ingredient of the proof is a variant of the Crossing Energy Theorem for Reeb flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Barcode Entropy of Reeb Flows Cineli, Erman Ginzburg, Viktor L. Gurel, Basak Z. Mazzucchelli, Marco Symplectic Geometry Dynamical Systems 53D40, 37B40, 37J12, 37J55 In this paper we continue investigating connections between Floer theory and dynamics of Hamiltonian systems, focusing on the barcode entropy of Reeb flows. Barcode entropy is the exponential growth rate of the number of not-too-short bars in the Floer or symplectic homology persistence module. The key novel result is that the barcode entropy is bounded from below by the topological entropy of any hyperbolic invariant set. This, combined with the fact that the topological entropy bounds the barcode entropy from above, established by Fender, Lee and Sohn, implies that in dimension three the two types of entropy agree. The main new ingredient of the proof is a variant of the Crossing Energy Theorem for Reeb flows. |
| title | On the Barcode Entropy of Reeb Flows |
| topic | Symplectic Geometry Dynamical Systems 53D40, 37B40, 37J12, 37J55 |
| url | https://arxiv.org/abs/2401.01421 |