Anosov Structure on Margulis Space Time

TL;DR

This paper investigates the dynamical properties of Margulis Space Times, demonstrating the existence of Anosov structures and contraction behaviors in geodesic flows, and establishing connections to Anosov representations in non semi-simple Lie groups.

Contribution

It introduces the stable and unstable leaves for geodesic flow on Margulis Space Times and proves their contraction properties, linking monodromy to Anosov representations in non semi-simple Lie groups.

Findings

Identification of stable and unstable leaves for geodesic flow.

Proof of contraction properties of leaves under flow.

Monodromy of Margulis Space Times as Anosov representations.

Abstract

In this paper we describe the stable and unstable leaves for the geodesic flow on the space of non-wandering spacelike geodesics of a Margulis Space Time and prove contraction properties of the leaves under the flow. We also show that monodromy of Margulis Space Times are "Anosov representations in non semi-simple Lie groups".