Dimension gap and variational principle for Anosov representations

Abstract

We consider a representation of a finitely generated CAT(--K) group $\Gamma$ in SL(d, R) that is Zariski dense and k-Anosov for at least two values of k. We exhibit a gap for the Minkowski dimension of minimal sets for the action of $\Gamma$ on flags spaces. The proof uses a variational principle for the action on partial flags.

This paper replaces ''Dimension gap for the limit sets of Anosov representations''. The use of Connel-Muchnik 07 in the proof of the variational principle was erroneous. In this new version, we directly prove the variational principle Theorem 1.7

References in corpus (3)

• Exponential bounds for random walks on hyperbolic spaces without moment conditions
• Anosov representations with Lipschitz limit set
• Exact dimension of dynamical stationary measures