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On the ergodicity of geodesic flows

Published online by Cambridge University Press:  19 September 2008

W. Ballmann  and
M. Brin
W. Ballmann
Affiliation:
Department of Mathematics, University of Bonn, 5300 Bonn 1, Germany and University of Maryland
M. Brin
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
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Abstract

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In this paper we study the ergodic properties of the geodesic flows on compact manifolds of non-positive curvature. We prove that the geodesic flow is ergodic and Bernoulli if there exists a geodesic γ such that there is no parallel Jacobi field along γ orthogonal to γ. In particular, this is true if there exists a tangent vector v such that the sectional curvature is strictly negative for all two-planes containing v, or if there exists a tangent vector v such that the second fundamental form of the horosphere determined by v is definite at the support of v.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 3-4 , December 1982 , pp. 311 - 315
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

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