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We establish an extension of the Hopf-Tsuji-Sullivan dichotomy to any Zariskidense discrete subgroup of a semisimple real algebraic group $G$. We then applythis dichotomy to Anosov subgroups of $G$, which surprisingly presents adifferent phenomenon depending on the rank of the ambient group $G$.

The Hopf-Tsuji-Sullivan dichotomy in higher rank and applications to Anosov subgroups