Chappell, M. J. (Michael J.) (1987) Lyapunov exponents for certain stochastic flows. PhD thesis, University of Warwick.

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Abstract

This thesis examines the asymptotic behaviour of solution flows of certain stochastic differential equations utilising the theory of Lyapunov exponents. The approach is taken on two fronts. Initially flows are considered on compact manifolds that arise from embedding the manifold in some Euclidean space - the Gradient Brownian flow. In this case the existence of the Lyapunov exponents is known. Results are obtained for the sum of the exponents - which has the geometrical interpretation as the exponential rate of change of volume under the action of the flow - and for the largest exponent on generalised Clifford Tori and convex hypersurfaces.

The situation on non-compact manifolds is then considered - where the existence of the exponents is uncertain due to the fact that the existence of a finite invariant measure is not guaranteed. However, by considering a stochastic mechanical system this problem is overcome and conditions for existence are obtained for both the Lyapunov spectrum and the sum' of the exponents. Some examples are then considered in the noncompact case.

Finally in the Appendix a computational method for calculating the largest Lyapunov exponent on a hypersurface is considered.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Lyapunov exponents, Stochastic processes
Official Date:	1987
Dates:	Date Event 1987 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Elworthy, K. D.
Extent:	iii, 188 leaves
Language:	eng

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