Hyperbolic behaviour of geodesic flows on manifolds with no focal points
- 1 March 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 3 (1) , 1-12
- https://doi.org/10.1017/s0143385700001796
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- Geodesic Flows on Negatively Curved Manifolds. IITransactions of the American Mathematical Society, 1973
- Geodesic Flow in Certain Manifolds Without Conjugate PointsTransactions of the American Mathematical Society, 1972