Chapter 1 will more formally introduce and explain shadowing.
Chapter 2 is the main body of the work, which introduces the optimizations to
the shadowing algorithm of Quinlan and Tremaine [29],
and talks about high-dimensional
shadowing in general. Chapter 3
contains some preliminary results on high-dimensional shadowing
that will be of interest both to practicing *N*-body astronomers,
and to those interested in shadowing in general.
Chapter 4 contains descriptions of the many open questions and further
avenues of research in this area.
The appendix contains a review of the basic *N*-body equations and
the derivation of the Jacobian of an *N*-body system
in which *M* particles move amongst *N*-*M* fixed ones.

Sun Dec 29 23:43:59 EST 1996

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