Positive topological entropy for Reeb flows on 3-dimensional Anosov contact manifolds

Let $(M, ξ)$ be a compact contact 3-manifold and assume that there exists a contact form $α_0$ 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.

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