Although chaotic dynamics had been known to exist for a long time, its
importance for a broad variety of applications began to be widely
appreciated only within the last decade or so. Concurrently, there has
been enormous interest both within the mathematical community and
among engineers and scientists. The field continues to develop rapidly in
many directions, and its implications continue to grow. Naturally, such a
situation calls for textbooks to serve the need of providing courses to
students who will eventually utilize concepts of chaotic dynamics in their
future careers. A variety of chaos texts now exists. In my teaching of
several courses on chaos, however, I found that the existing texts were not
altogether suitable for the type of course I was giving, with respect to both
level and coverage of topics. Hence I was motivated to prepare and
circulate notes for my class, and these notes led to this book. The book is
intended for use in a graduate course for scientists and engineers.
Accordingly, any mathematical concepts that such readers may not be
familiar with (e.g., measure, Cantor sets, etc.) are introduced and
informally explained as needed. While the intended readers are not
mathematicians, there is a greater emphasis on basic mathematical
concepts than in most other books that address the same audience. The
style is pedagogical, and it is hoped that the very interesting, sometimes
difficult, concepts that are the backbone for studies of chaos are made
clear. The coverage is broad, including such topics as multifractals,
quantum chaos, embedding, chaotic scattering, etc. Thus the book can
also serve as a reference for workers in the field. There is too much in this
book for a single one semester course. Hence it is expected that a teacher
would select parts in designing a course; for example, one choice might be
to base a one semester introductory course on Chapters 1-4, possibly
supplemented by a few sections from later chapters. The author has also
taught more advanced courses that utilized material now contained in
Chapter 7, 9 and 10, supplemented by readings from current research
papers.