I thank my supervisor, Prof. Ken Jackson, for many insightful conversations during the development of the ideas in this thesis, and for helpful comments on the text. My second reader, Dr. Min Hu, also made many helpful suggestions.
I thank Gerry Quinlan and Scott Tremaine for the paper that inspired this thesis, as well as for the many discussions carried on long-distance via e-mail. Gerry also provided me with his original shadowing refinement code, and a postscript version of his figure 6.All this was only possible because of the Internet, so I'd like to thank all the organizations worldwide responsible for its upkeep.
My mother has been an inspiration throughout my life. She has always supported my dreams and aspirations, and if I do say so myself, I think she did a fine job raising me. I'd like to thank her for all she is, and all she has done for me.
I would like to thank Prof. Mart Molle, my supervisor during my foray into Computer Networks, for his wisdom, friendship, understanding, and for teaching me how to be a (successful?) researcher. Thanks, ``Dad''.
I thank Nick Trefethen for being a good devil's advocate, and Wayne Enright for offering his 7/8 pair explicit Runge-Kutta integrator, although I haven't used it yet.
For financial support, I thank the Department of Computer Science and its professors at the University of Toronto. Computer time for the simulations and shadowing runs performed in this thesis were provided in part by Fujitsu Canada, the High Performance Computing Centre of Calgary, and the University of Calgary. The University of Toronto's Computing Disciplines Facility (CDF) and Department of Computer Science Labs provided local computer facilities.
Finally, I'd like to thank Robert M. Pirsig, author of the book Lila, for his ``slips of paper'' method of organization. The method consists of transcribing each individual idea onto one slip of paper, and then organizing all the slips of paper into a good order of presentation. This has the advantage that there is no need to start with a ``master plan'', or even an outline. The ideas organize themselves, and soon you begin to ``notice'' what certain piles of slips are about; then you give that pile a title; piles of piles then organize themselves into sections and chapters; then you are done. This method allowed me to organize the ideas herein with fine-grained detail in only 8 days; writing the thesis was then an O(n) process, with n being the number of slips. Transcribing the slips into LaTeX took just over 2 weeks, followed by 1 week of editing and brushing up. I'm told this is quite a short time to write up a Master's thesis. I would highly recommend this method to anybody writing up a large work, especially the first time. In fact, I'd highly recommend the entire book to anybody.