  Let $(M, \xi)$ be a compact contact 3-manifold and assume that there exists a
contact form $\alpha_0$ on $(M, \xi)$ whose Reeb flow is Anosov. We show this
implies that every Reeb flow on $(M, \xi)$ has positive topological entropy.
Our argument builds on previous work of the author
(http://arxiv.org/abs/1410.3380) and recent work of Barthelm\'e 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.
