``What shadows we are, and what shadows we pursue.''

-- Edmund Burke, *Speech*. (1780)

*
The main thrust of this thesis is to extend a previously published
numerical shadowing refinement procedure to make it more efficient,
thus allowing larger and more realistic systems to be shadowed. The
astrophysical N-body problem is used as an example, although the
refinement procedure could just as easily be used on any chaotic
system. With various numerical tricks and physical
insights, our algorithm runs, depending on the problem, between 5 and
100 times faster than the original algorithm.
*

Sun Dec 29 23:43:59 EST 1996

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