2023/08/11 by Matthias Meiwes, Meiwes, Matthias
Computer Science · Mathematics · #37B10 #37C10 #53D42 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2308.06047
openalex publication_date 2023/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we exhibit certain linking properties of periodic orbits of C1+α flows with positive topological entropy on closed 3-manifolds M. It is shown that any such flow contains a link L of periodic orbits and a horseshoe K in MŁ, such that all periodic orbits in K are unique in their homotopy class in MŁ(among periodic orbits in M). Moreover, the entropy of the flow can be approximated by the entropies of such horseshoes K. A version of that result for chords is obtained. Our main motivation comes from Reeb dynamics, and as an application, we address a question by Alves-Pirnapasov, and obtain that the topological entropy of a 3-dimensional, C∞-generic Reeb flow can be approximated by the exponential homotopical growth rates of contact homology in link complements.