Summary
In this article we develop a method of deriving asymptotic formulae for the orbital counting function for the action of certain discrete groups of isometries of simply connected negatively curved manifolds. We consider the particular case of normal subgroupsΓ ⊲Γ 0 of a co-compact groupΓ 0 for which the quotientΓ 0/Γ ≌ ℤk. Even in the special case of manifolds ofconstant negative curvature, this leads to new results. In particular, we have asymptotic estimates for some groups which arenot geometrically finite.
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Oblatum III-1993 & 18-VIII-1993
The first author was supported by The Royal Society through a University Research Fellowship. The second author was supported by the UK SERC under grant number GR/G51930
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Pollicott, M., Sharp, R. Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature. Invent Math 117, 275–302 (1994). https://doi.org/10.1007/BF01232242
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DOI: https://doi.org/10.1007/BF01232242