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Lyapunov exponents for a stochastic analogue of the geodesic flow

Authors: A. P. Carverhill and K. D. Elworthy
Journal: Trans. Amer. Math. Soc. 295 (1986), 85-105
MSC: Primary 58G32; Secondary 58F11, 60H10
MathSciNet review: 831190
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Abstract: 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.

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Keywords: Lyapunov exponents, geodesic flow, stochastic differential equations, Brownian motion, Riemannian manifolds, hyperbolic space, horocycles
Article copyright: © Copyright 1986 American Mathematical Society