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Title: Lyapunov exponents for certain stochastic flows
Author: Chappell, Michael John
ISNI:       0000 0001 2416 6919
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1987
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics