Barcode entropy of geodesic flows
| Autor: | Ginzburg, Viktor L., Gurel, Basak Z., Mazzucchelli, Marco |
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| Přispěvatelé: | University of California [Santa Cruz] (UC Santa Cruz), University of California (UC), University of Central Florida [Orlando] (UCF), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Differential Geometry
Differential Geometry (math.DG) Mathematics - Symplectic Geometry [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] FOS: Mathematics Symplectic Geometry (math.SG) 37D40 37B40 58E10 Dynamical Systems (math.DS) Mathematics - Dynamical Systems [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] |
| Popis: | We introduce and study the barcode entropy for geodesic flows of closed Riemannian manifolds, which measures the exponential growth rate of the number of not-too-short bars in the Morse-theoretic barcode of the energy functional. We prove that the barcode entropy bounds from below the topological entropy of the geodesic flow and, conversely, bounds from above the topological entropy of any hyperbolic compact invariant set. As a consequence, for Riemannian metrics on surfaces, the barcode entropy is equal to the topological entropy. A key to the proofs and of independent interest is a crossing energy theorem for gradient flow lines of the energy functional. Comment: 41 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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