Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Baxendale, Brownian motions in the diffeomorphism group I, Compositio Math. 53 (1984), 19–50.
P. Baxendale and T.E. Harris, Isotropic stochastic flows, Ann. Probab. (to appear).
A.P. Carverhill, Flows of stochastic dynamical systems: ergodic theory, Stochastics 14 (1985), 273–318.
A.P. Carverhill, A formula for the Lyapunov numbers of a stochastic flow. Application to a perturbation theorem, Stochastics 14 (1985), 209–226.
A.P. Carverhill, M.J. Chappell and K.D. Elworthy, Characteristic exponents for stochastic flows, To appear in the Proceedings of BIBOS I: Stochastic processes-Mathematics and Physics, Bielefeld, September 1984.
M.J. Chappell, Bounds for average Lyapunov exponents of gradient stochastic systems, Proceedings of Workshop on Lyapunov Exponents, Bremen, November 1984 (this volume).
K.D. Elworthy, Stochastic differential equations on manifolds, Cambridge University Press, 1982.
K.D. Elworthy and D. Stroock, Large deviation theory for mean exponents of stochastic flows, Appendix to reference [5] above.
H. Föllmer, An entropy approach to the time reversal of diffusion processes, Proceedings of 4th IFIP Conference on Stochastic Differential Systems, Lecture Notes in Control and Information Sciences 69 (1984), 156–163.
H. Furstenberg, Noncommuting random products, Trans. Amer. Math. Soc. 108 (1963), 377–428.
F.R. Gantmacher, The theory of matrices, Vol. I, Chelsea, New York, 1959.
K. Ichihara and H. Kunita, A classification of second order degenerate elliptic operators and its probabilistic characterization, Z. Wahrsch. Verv. Gebiete 30 (1974), 235–254.
N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North Holland, Amsterdam, 1981.
S. Kobayishi and K. Nomizu, Foundations of differential geometry, Vol. II, Interscience, New York, 1963.
H. Kunita, Stochastic differential equations and stochastic flow of diffeomorphisms, École d'Été de Probabilités de Saint-Flour XII, Lecture notes in mathematics 1097 (1984), 143–303.
Y. Le Jan, Exposants de Lyapunov pour les mouvements browniens isotropes, C.R. Acad. Sci. Paris Sér. I Math. 299 (1984), 947–949.
A. Rényi, On measures of entropy and information, 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. I (1960), 547–561.
D. Ruelle, Ergodic theory of differentiable dynamical systems, Inst. Hautes Etudes Sci. Publ. Math. 50 (1979), 275–305.
K. Yosida, Functional analysis, (6th ed.), Springer-Verlag, Berlin, 1980.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Baxendale, P.H. (1986). The Lyapunov spectrum of a stochastic flow of diffeomorphisms. In: Arnold, L., Wihstutz, V. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076851
Download citation
DOI: https://doi.org/10.1007/BFb0076851
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