A First Course in Chaotic Dynamical Systems: Theory and Experiment

A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton’s method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented.Chaotic Dynamical Systems Software, Labs 1–6 is a supplementary laboratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems, it leads to a rich understanding of this emerging field.

Written by one of the most respected mathematicians in the field, this book conveys the essential mathematical ideas in dynamical systems using a combination of theory and computer experimentation. This introductory look at dynamical systems includes investigating the rates of approach to attracting and indifferent fixed points to the discovery of Feigenbaum's constant; exploring the window structure in the orbit diagram; and understanding the periods of the bulbs in the Mandelbrot set.

This is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton’s method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented.

Professor Robert L. Devaney received his A.B. from Holy Cross College and his Ph.D. from the University of California at Berkeley in 1973. He taught at Northwestern University, Tufts University, and the University of Maryland before coming to Boston University in 1980. He served there as chairman of the Department of Mathematics from 1983 to 1986. His main area of research is dynamical systems, including Hamiltonian systems, complex analytic dynamics, and computer experiments in dynamics. He is the author of An Introduction to Chaotic Dynamical Systems, and Chaos, Fractals, and Dynamics: Computer Experiments in Modern Mathematics, which aims to explain the beauty of chaotic dynamics to high school students and teachers.