Chaos

Aimed at fellow applied mathematicians, this textbook introduces chaos and nonlinear dynamics. It seeks a balance between the precision valued by mathematicians and the practical outlook of physicists.

The core ideas appear in many other volumes, but this one stands apart through its reflective, philosophical stance, its wide scope, its brevity, its detours into less travelled intellectual territory, and its generous, instructive illustrations.

Written at graduate level, the book sometimes moves beyond standard theory toward newer lines of thought, occasionally through its exercises. It traces the subject's development from Poincaré onward and covers maps, homoclinic bifurcations, Hamiltonian systems, and more unusual topics such as Julia and Mandelbrot sets. An appendix describes some of the more involved programs used to generate the figures.

The material grew out of lectures given to upper undergraduates and beginning graduate students, which makes it well suited to courses at that level. Each chapter comes with exercises spanning a range of difficulty.