Barcode entropy for Reeb flows on contact manifolds with Liouville fillings

2023/05/31 by Elijah Fender, Sangjin Lee, Beomjun Sohn
Computer Science · Mathematics · #Barcode #Computer science #Entropy (arrow of time) #Mathematical Dynamics and Fractals #Mathematics #Physics #Pure mathematics #Reinforcement Learning in Robotics #Topological and Geometric Data Analysis

paper · doi:10.1142/s0219199725500440

openalex publication_date 2025/03/20 · crossref created 2025/03/20 · crossref issued 2025/04/24 · crossref published 2025/04/24 · crossref published-online 2025/04/24 · openalex created_date 2025/10/10 · crossref deposited 2026/01/28 · crossref published-print 2026/04/01 · openalex updated_date 2026/08/01 · crossref indexed 2026/08/06

Abstract

We study the topological entropy of Reeb flows on contact manifolds with Liouville fillings. With the theory of persistence modules, we define [Formula: see text]-barcode entropy from the symplectic homology of a filling. We prove that the [Formula: see text]-barcode entropy is independent of the choice of the filling and that the barcode entropy provides a lower bound for the topological entropy of the Reeb flow.

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