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

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 3 , September 1991 , pp. 577 - 582
Copyright
Copyright © Cambridge University Press 1991

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References

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