Skewed Anosov flows are orbit equivalent to Reeb-Anosov flows in dimension 3

TL;DR

This paper demonstrates that in three dimensions, skewed Anosov flows are orbit equivalent to Reeb-Anosov flows, characterizes invariant contact forms via linking numbers, and establishes open book decompositions for Reeb-Anosov flows.

Contribution

It establishes orbit equivalence between skewed Anosov flows and Reeb-Anosov flows in dimension 3, and provides new characterizations and decompositions related to these flows.

Findings

Skewed Anosov flows are orbit equivalent to Reeb-Anosov flows in dimension 3.

Invariant contact forms are characterized by linking numbers between invariant measures.

Existence of open book decompositions with one boundary component for Reeb-Anosov flows.

Abstract

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