Applications of Dynamics to Compact Manifolds of Negative Curvature

François Ledrappier
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François Ledrappier: École Polytechnique, CNRS, Centre de Mathématiques

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 1195-1202 from Springer

Abstract: Abstract Consider closed Riemannian manifolds with negative sectional curvature. There are three natural dynamics associated with the Riemannian structure: the geodesic flow on the unit tangent bundle, the dynamics of the invariant foliations of the geodesic flow, and the Brownian motion on the universal cover of the manifold. These dynamics define global asymptotic objects such as growth rates or measures at infinity. For locally symmetric negatively curved spaces, these objects are easy to compute and to describe. In this paper, we survey some of their properties and relations in the general case.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-9078-6_113

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DOI: 10.1007/978-3-0348-9078-6_113

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