2015/12/10 by Marcelo R. R. Alves, Alves, Marcelo R. R. · 1 citation
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
paper · pdf · doi:10.48550/arxiv.1512.03140
openalex publication_date 2015/12/10 · 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\ncontact form \α0 on (M, \ξ) whose Reeb flow is Anosov. We show this\nimplies that every Reeb flow on (M, \ξ) has positive topological entropy.\nOur argument builds on previous work of the author\n(http://arxiv.org/abs/1410.3380) and recent work of Barthelm 'e and Fenley\n(http://arxiv.org/abs/1505.07999).\n This result combined with the work of Foulon and Hasselblatt\n(http://www.tufts.edu/as/math/Preprints/FoulonHasselblattLegendrian.pdf) is\nthen used to obtain the first examples of hyperbolic contact 3-manifolds on\nwhich every Reeb flow has positive topological entropy.\n