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.
Keywords
rank one space, Bowen–Margulis measure, mixing,
equidistribution, orbit counting function
