2015/12/10 by Marcelo R. R. Alves, Alves, Marcelo R. R. · 2 citations
Computer Science · Mathematics · #53D42 37J05 37D20 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis #math.DS #math.SG #msc:37D20 #msc:37J05 #msc:53D42
paper · pdf · doi:10.48550/arxiv.1512.03140
18 pages. Comments wellcome! arXiv admin note: text overlap with arXiv:1410.3380
arxiv created 2015/12/10 · openalex publication_date 2015/12/10 · arxiv updated 2015/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (M, ξ) be a compact contact 3-manifold and assume that there exists a contact form α0 on (M, ξ) whose Reeb flow is Anosov. We show this implies that every Reeb flow on (M, ξ) has positive topological entropy. Our argument builds on previous work of the author (http://arxiv.org/abs/1410.3380) and recent work of Barthelmé and Fenley (http://arxiv.org/abs/1505.07999). This result combined with the work of Foulon and Hasselblatt (http://www.tufts.edu/as/math/Preprints/FoulonHasselblattLegendrian.pdf) is then used to obtain the first examples of hyperbolic contact 3-manifolds on which every Reeb flow has positive topological entropy.