Abstract
Let be a proper, geodesically complete Hadamard space, and a discrete subgroup of isometries of with the fixed point of a rank one isometry of in its infinite limit set. In this paper we prove that if has nonarithmetic length spectrum, then the Ricks–Bowen–Margulis measure — which generalizes the well-known Bowen–Margulis measure in the CAT setting — is mixing. If in addition the Ricks–Bowen–Margulis measure is finite, then we also have equidistribution of -orbit points in , which in particular yields an asymptotic estimate for the orbit counting function of . This generalizes well-known facts for nonelementary discrete isometry groups of Hadamard manifolds with pinched negative curvature and proper CAT-spaces.
Citation
Gabriele Link. "Equidistribution and counting of orbit points for discrete rank one isometry groups of Hadamard spaces." Tunisian J. Math. 2 (4) 791 - 839, 2020. https://doi.org/10.2140/tunis.2020.2.791
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