xvi Preface I would also like to thank three professors under whom I studied while a grad- uate student: Charles Pugh, Morris Hirsch, and Stephen Smale. These people introduced me to the subject of dynamical systems and taught me many of the ideas and methods that I have used throughout my career. Many of my colleagues at Northwestern have also deeply influenced me in different ways: these people include John Franks, Donald Saari, and Robert Williams. I thank the following reviewers for their comments and useful suggestions for improvement of the manuscript: John Alongi, Pomona College Pau Atela, Smith College Peter Bates, Brigham Young University Philip Bayly, Washington University Michael Brin, University of Maryland Roman Grigoriev, Georgia Technological Institute Palle Jorgensen, University of Iowa Randall Pyke, Ryerson University Joel Robbin, University of Wisconsin Bjorn Sandstede, Ohio State University Douglas Shafer, University of North Carolina at Charlotte Milena Stanislavova, University of Kansas Franz Tanner, Michigan Technological University Howard Weiss, Pennsylvania State University I also thank Miguel Lerma for help in solving various LTEX A and graphics prob- lems, Marian Gidea for help with Adobe Illustrator, and Kamlesh Parwani for help with some Maple worksheets. I gratefully acknowledge the photograph by Julio Ottino and Paul Swanson used on the cover of the first edition of the book depicting mixing of fluids. This photo had previously appeared in the article [Ott89b]. A brief discussion of his research is given in Section 11.5.4. Most of all, I am grateful to my wife Peggie, who endured, with patience, understanding, and prayer, the ups and downs of writing this book from inception to conclusion. R. Clark Robinson clark@math.northwestern.edu October 2003
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