## Equidistribution and counting of orbit points for discrete rank one isometry groups of Hadamard spaces. (arXiv:1808.03223v1 [math.GR])

Let \$X\$ be a proper, geodesically complete Hadamard space, and \$\ \Gamma<\mbox{Is}(X)\$ a discrete subgroup of isometries of \$X\$ with the fixed point of a rank one isometry of \$X\$ in its infinite limit set. In this paper we prove that if \$\Gamma\$ has non-arithmetic length spectrum, then the Ricks' Bowen-Margulis measure -- which generalizes the well-known Bowen-Margulis measure in the CAT\$(-1)\$ setting -- is mixing. If in addition the Ricks' Bowen-Margulis measure is finite, then we also have equidistribution of \$\Gamma\$-orbit points in \$X\$, which in particular yields an asymptotic estimate for the orbit counting function of \$\Gamma\$. This generalizes well-known facts for non-elementary discrete isometry groups of Hadamard manifolds with pinched negative curvature and proper CAT\$(-1)\$-spaces. 查看全文>>