Strongly adapted contact geometry of Anosov 3-flows

TL;DR

This paper characterizes Anosov 3-flows using contact geometry and Reeb dynamics, revealing the topological structure of the space of such geometries and proving a key synchronization theorem.

Contribution

It introduces a contact geometric framework for Anosov 3-flows and establishes the homotopy equivalence of the geometry space to the flow space, along with a novel synchronization theorem.

Findings

The space of adapted contact geometries is homotopy equivalent to the space of Anosov 3-flows.

A technical theorem on asymptotic synchronization of adapted norms is proved.

The approach links contact geometry with dynamical properties of Anosov flows.

Abstract

We provide a 3 dimensional contact geometric characterization of Anosov 3-flows based on interactions with Reeb dynamics. We investigate basic properties of the space of the resulting geometries and in particular show that such space is homotopy equivalent to the space of Anosov 3-flows. A technical theorem on the asymptotic synchronization of adapted norms is proved, which can be of broader interest.