Topological entropy for Reeb vector fields in dimension three via open book decompositions

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Given an open book decomposition of a contact three man-ifold (M, ξ) with pseudo-Anosov monodromy and fractional Dehn twist coefficient c = k n, we construct a Legendrian knot Λ close to the stable foliation of a page, together with a small Legendrian pushoff Λ. When k ≥ 5, we apply the techniques of [CH2] to show that the strip Legen-drian contact homology of Λ → Λ is well-defined and has an exponential growth property. The work [Al2] then implies that all Reeb vector fields for ξ have positive topological entropy.