Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology

TL;DR

This paper explores the symplectic and contact geometric structures underlying Anosov flows in three dimensions, providing new characterizations and frameworks for understanding their dynamics through geometric topology.

Contribution

It introduces a contact and symplectic geometric framework for Anosov flows and discusses uniqueness and characterization results based on Reeb flows.

Findings

Characterization of Anosov flows via contact and symplectic geometry

Uniqueness results for bi-contact structures associated with Anosov flows

Reeb flow-based criteria for Anosovity

Abstract

We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and discuss a framework to use tools from contact and symplectic geometry and topology in the study of Anosov dynamics. We also discuss some uniqueness results regarding the underlying (bi)-contact structures for an Anosov flow and give a characterization of Anosovity based on Reeb flows.