# Patterson-Sullivan theory for Anosov subgroups

## TL;DR

This paper generalizes Patterson-Sullivan theory to Anosov subgroups in higher rank Lie groups, establishing a link between Hausdorff dimensions of limit sets and Finsler critical exponents.

## Contribution

It extends classical Patterson-Sullivan results to higher rank settings using invariant Finsler metrics and establishes a key equality for Anosov subgroups.

## Key findings

- Hausdorff dimension of flag limit sets equals Finsler critical exponents
- Extension of Patterson-Sullivan theory to higher rank semisimple Lie groups
- Use of invariant Finsler metrics on symmetric spaces

## Abstract

We extend several notions and results from the classical Patterson-Sullivan theory to the setting of Anosov subgroups of higher rank semisimple Lie groups, working primarily with invariant Finsler metrics on associated symmetric spaces. In particular, we prove the equality between the Hausdorff dimensions of flag limit sets, computed with respect to a suitable Gromov (pre-)metric on the flag manifold, and the Finsler critical exponents of Anosov subgroups.