The most advanced technology has been used to photograph and reproduce this manuscript from the microfîhn master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough,

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... margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white This study was pursued in a series of closely related papers of which we mention only four. Arnold and Kliemann (1987) and engaged in detailed investigations concerning the existence of a unique invariant probability measure, a crucial step in this approach. Arnold et ai. (1986b) and Arnold and Kliemann (1986) pursued a finer study of the system's stability properties using the notion of moment Lyapunov exponents and large deviation theory.