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We prove that in dimension 3, Anosov flows which are 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.
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Théo Marty (2025) studied this question.
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