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Examples of discrete groups of hyperbolic motions conservative but not ergodic at infinity

Published online by Cambridge University Press:  19 September 2008

Masahiko Taniguchi
Affiliation:
Department of Mathematics, Kyoto University, Japan
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Abstract

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For every n ≥ 2, a discrete subgroup of isometries of the hyperbolic n-space, which is conservative but not ergodic on the sphere at infinity, is constructed.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1988

References

REFERENCES

[1]Agard, S.. A geometric proof of Mostow's rigidity theorem for groups of divergence type. Acta Math. 151 (1983), 231252.CrossRefGoogle Scholar
[2]Ahlfors, L.. Möbius transformations in several dimensions. Ordway Prof. Lectures in Math. (1981).Google Scholar
[3]Lyons, T. & Sullivan, D.. Function theory, random paths and covering spaces, J. Diff. Geom. 19 (1984), 299323.Google Scholar
[4]Millson, J.. On the first Betti number of a constant negatively curved manifold. Ann. of Math. 104 (1976), 235247.CrossRefGoogle Scholar
[5]Sullivan, D.. On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Ann. of Math. Studies 97 (1981), 465496.Google Scholar