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Hyperbolic behaviour of geodesic flows on manifolds with no focal points

Published online by Cambridge University Press:  19 September 2008

Keith Burns
Keith Burns
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901
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Abstract

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It is shown that the unit tangent bundle of a compact uniform visibility manifold with no focal points contains a subset of positive Liouville measure on which all the characteristic exponents of the geodesic flow (except in the flow direction) are non-zero. This completes Pesin's proof that the geodesic flow of such a manifold is Bernoulli.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 1 , March 1983 , pp. 1 - 12
Copyright
Copyright © Cambridge University Press 1983

References

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