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Let $X$ be a proper, geodesically complete Hadamard space, and $\\Gamma<\mbox{Is}(X)$ a discrete subgroup of isometries of $X$ with the fixedpoint of a rank one isometry of $X$ in its infinite limit set. In this paper weprove that if $\Gamma$ has non-arithmetic length spectrum, then the Ricks'Bowen-Margulis measure -- which generalizes the well-known Bowen-Margulismeasure 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 estimatefor the orbit counting function of $\Gamma$. This generalizes well-known factsfor non-elementary discrete isometry groups of Hadamard manifolds with pinchednegative curvature and proper CAT$(-1)$-spaces.

Equidistribution and counting of orbit points for discrete rank one isometry groups of Hadamard spaces