Variation of the Liouville measure of a hyperbolic surface
ERGODIC THEORY AND DYNAMICAL SYSTEMS, vol.23, pp.729-758, 2003 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 23
- Publication Date: 2003
- Doi Number: 10.1017/s0143385702001463
- Journal Name: ERGODIC THEORY AND DYNAMICAL SYSTEMS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.729-758
- Hacettepe University Affiliated: No
Abstract
For a compact Riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the Riemannian metric defines a natural transverse measure to this foliation, the Liouville transverse measure, which does depend on the metric. For a surface S, we show that the map which to a hyperbolic metric on S associates its Liouville transverse measure is differentiable, in an appropriate sense. Its tangent map is valued in the space of transverse Holder distributions for the geodesic foliation.