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The action at infinity of conservative groups of hyperbolic motions need not have atoms

Published online by Cambridge University Press:  19 September 2008

John A. Velling
Department of Mathematics, Brooklyn College, City University of New York, Brooklyn, New York 11210, USA
Katsuhiko Matsuzaki
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan


Herein the authors show that discrete groups of motions on Hn+1 may be conservative on Sn but have no positive measure ergodic components for this boundary action. An explicit example of such a group is given for H3 using the Apollonian circle packing of R2.

Research Article
Copyright © Cambridge University Press 1991

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