Keywords
- Lyapunov Exponent
- Stochastic System
- Stable Manifold
- Geodesic Flow
- Lyapunov Spectrum
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baxendale, P.H. Brownian Motions in the Diffeomorphism Group 1. Compositio Mathematica 53 p. 19–50 (1984).
Baxendale, P.H. Asymptotic Behaviour of Stochastic Flows of Diffeomorphisms: Two Case Studies. Preprint, Department of Mathematics, The University, Aberdeen AB9 2TY, Scotland.
Baxendale, P.H. Lyapunov Spectrum of a Stochastic Flow of Diffeomorphisms. This volume.
Baxendale, P.H. and Harris, T.E. Isotropic Stochastic Flows. Preprint, Universities of Aberdeen, Scotland and Southern California, U.S.A. 1985.
Carverhill, A.P. Flows of Stochastic Dynamical Systems: Ergodic Theory. Stochastics 14 p. 273–318 (1985).
Carverhill, A.P. A Formula for the Lyapunov Numbers of a Stochastic Flow. Application to a Perturbation Theorem. Stochastics 14 p. 209–226 (1985).
Carverhill, A.P. A Markovian Approach to the Multiplicative Ergodic (Oseledec) Theorem for Nonlinear Stochastic Dynamical Systems. Preprint, Mathematics Institute, University of Warwick, Coventry, England.
Carverhill, A.P. Furstenberg's Theorem for Nonlinear Stochastic Systems. Preprint, Warwick, 1985.
Carverhill, A.P. and Elworthy, K.D. Flows of Stochastic Dynamical Systems: The Functional Analytic Approach. Z. Wahsch Verw. Gebiete 65, 245–267 (1983).
Carverhill, A.P. and Elworthy, K.D. Lyapunov Exponents for a Stochastic Analogue of the Geodesic Flow. Preprint, Mathematics Institute, Warwick University, Coventry CV4 7AL, England.
Carverhill, A.P., Chappell, M.J. and Elworthy, K.D. Characteristic Exponents for Stochastic Flows. Proceedings of BIBOS 1: Stochastic Processes. Bielefeld, September 1984. Lecture Notes in Mathematics, Springer-Verlag.
Chappell, M.J. Lyapunov Exponents for Gradient Brownian Systems on the Circle. Research Report, Mathematics Institute, University of Warwick, Coventry CV4 7AL England.
Chappell, M.J. Bounds for Average Lyapunov Exponents of Gradient Stochastic Systems. This volume.
Elworthy, K.D. Stochastic Differential Equations on Manifolds. L.M.S. Lecture Notes. Cambridge University Press 1982.
Elworthy, K.D. Stochastic Dynamical Systems and Their Lyapunov Exponents. Proceedings of ELAM VII, Simon Bolivar University, Caracus, Venezuela, July, 1984. Lecture Notes in Mathematics. Springer-Verlag.
Furstenberg, H. Noncommuting Random Products. Transactions AMS 108 (1963).
Furstenberg, H. and Kifer, Yu. Random Matrix Products and Measures on Projective Spaces. Israel Journal of Mathematics 46 (1983).
Ichihara, K. and Kunita H. A Classification of the Second Order Degenerate Elliptic Operators and its Probabilistic Characterization. Z. Wahsch Verw. Gebiete 30 p. 235–254 (1974).
le Jan, Y. On Isotropic Brownian Motions, Preprint, Université Paris 6, France. 1984.
le Jan, Y. Equilibre et Exposants de Lyapunov de Certains Flots Browniens. C.R. Acad. Sciences Paris t. 298 Série 1. 361–364 (1984).
Khas'minskii, R.Z. Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Systems. Th. Prob. Appl. 12. 144–147 (1967).
Khas'minskii, R.Z. Stochastic Stability of Differential Equations. Sijthoff and Noordhoff. Alphen aan den Rijn. The Netherlands. 1980 (Originally in Russian: Moscow: Nauka, 1969).
Kifer, Yu. A Multiplicative Ergodic Theorem for Random Transformations. Preprint, Hebrew University of Jerusalem. (1984).
Kifer, Yu. This Volume.
Ruelle, D. Ergodic Theory of Differentiable Dynamical Systems. Publications IHES 50 275–305 (1979).
Ventsel, A.D. and Freidlin, M.I. On Small Random Perturbations of Dynamical Systems. Russian Mathematical Surveys 25, 1–56 (1970).
Ventsel, A.D. and Freidlin, M.I. Random Perturbations of Dynamical Systems. Grundlehren der Math Wiss. 260 Springer (1984).
Yosida, K. Functional Analysis (3rd Edition). Springer Verlag, 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Carverhill, A. (1986). Survey: Lyapunov exponents for stochastic flows on manifolds. In: Arnold, L., Wihstutz, V. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076849
Download citation
DOI: https://doi.org/10.1007/BFb0076849
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16458-6
Online ISBN: 978-3-540-39795-3
eBook Packages: Springer Book Archive
