Skewed Anosov flows in dimension 3 are Reeb-like

Abstract

We prove that in dimension 3, Anosov flows which are $\mathbb{R}$-covered and skewed are orbit equivalent to Reeb–Anosov flows. A linking number between invariant signed measures is used to characterize the existence of an invariant contact form or of a Birkhoff section with a given boundary. We also prove the existence of open book decompositions with one boundary component for Reeb–Anosov flows.