Lyapunov exponents for a stochastic analogue of the geodesic flow

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)85-105
Journal / PublicationTransactions of the American Mathematical Society
Issue number1
Publication statusPublished - May 1986
Externally publishedYes


New invariants for a Riemannian manifold are defined as Lyapunov exponents of a stochastic analogue of the geodesic flow. A lower bound is given reminiscent of corresponding results for the geodesic flow, and an upper bound is given for surfaces of positive curvature. For surfaces of constant negative curvature a direct method via the Doob h-transform is used to determine the full Lyapunov structure relating the stable manifolds to the horocycles. © 1986 American Mathematical Society.

Research Area(s)

  • Brownian motion, Geodesic flow, Horocycles, Hyperbolic space, Lyapunov exponents, Riemannian manifolds, Stochastic differential equations