---
abstract: 'We study infinite covolume discrete subgroups of higher rank semisimple Lie groups, motivated by understanding basic properties of Anosov subgroups from various viewpoints (geometric, coarse geometric and dynamical). The class of Anosov subgroups constitutes a natural generalization of convex cocompact subgroups of rank one Lie groups to higher rank. Our main goal is to give several new equivalent characterizations for this important class of discrete subgroups. Our characterizations capture “rank one behavior” of Anosov subgroups and are direct generalizations of rank one equivalents to convex cocompactness. Along the way, we considerably simplify the original definition, avoiding the geodesic flow. We also show that the Anosov condition can be relaxed further by requiring only non-uniform unbounded expansion along the (quasi)geodesics in the group.'
author:
- 'Michael Kapovich, Bernhard Leeb, Joan Porti'
date: 'March 3, 2017'
title: |
    Anosov subgroups:\
    Dynamical and geometric characterizations
---

Introduction
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This paper is devoted to studying basic properties of Anosov subgroups of semisimple Lie groups from various viewpoints (geometric, coarse geometric and dynamical). The class of Anosov subgroups, introduced by Labourie [@Labourie] and further extended by Guichard and Wienhard [@GW], constitutes a natural generalization of convex cocompact subgroups of rank one Lie groups 