Patterson-Sullivan theory for Anosov subgroups

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.

Final version: Main notations were revised to reflect the dependence with the choice of $\bar{\theta }$. Section 10 was expanded, and two new appendices were added. To appear in the Transactions of the American Mathematical Society

References in corpus (3)

• Morse actions of discrete groups on symmetric space
• Relativizing characterizations of Anosov subgroups, I
• A combination theorem for Anosov subgroups

Cited by in corpus (3)

• Anosov representations with Lipschitz limit set
• Ergodicity and equidistribution in Hilbert geometry
• Dimension gap and variational principle for Anosov representations