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Journal of the London Mathematical Society 1987 s2-36(2):295-313; doi:10.1112/jlms/s2-36.2.295
© 1987 by London Mathematical Society
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© Oxford University Press

Atoms for Measures on the Limit Set of a Discrete Group

Peter J. Nicholls

Department of Mathematical Sciences, Northern Illinois University DeKalb, Illinois 60115, USA

Consideration is given to the atomic part of those measures constructed by Patterson and Sullivan on the limit set of a discrete group. It is shown that if the Poincaré series diverges at the critical exponent the measure has no atomic part. A parabolic fixed point of full rank cannot be an atom for the measure and a non-fixed point which is an atom must be a limit point to which orbits approach extremely tangentially.


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