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. © 1986 American Mathematical Society.
| Original language | English |
|---|---|
| Pages (from-to) | 85-105 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 295 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - May 1986 |
| Externally published | Yes |
Research Keywords
- Brownian motion
- Geodesic flow
- Horocycles
- Hyperbolic space
- Lyapunov exponents
- Riemannian manifolds
- Stochastic differential equations
Fingerprint
Dive into the research topics of 'Lyapunov exponents for a stochastic analogue of the geodesic flow'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver