Anosov representations over closed subflows

TL;DR

This paper generalizes Anosov representations by focusing on invariant closed geodesic subflows, broadening the class of representations with desirable geometric properties and establishing their fundamental characteristics.

Contribution

It introduces a new class of representations called Anosov over closed subflows, extending classical theory and providing multiple characterizations and properties.

Findings

Includes many non-discrete representations with good geometric properties

Provides equivalent characterizations of these generalized representations

Establishes stability, Cartan property, and regularity of limit maps

Abstract

We introduce a generalization of the notion of Anosov representations by restricting to invariant closed geodesic subflows. Examples of such representations include many non-discrete representations with good geometric properties, such as primitive-stable representations. We give several equivalent characterizations of this type of representations and prove some properties analogous to the classical Anosov representations, such as stability, the Cartan property and regularity properties of the limit maps.