Chaos: A Mathematical Introduction

Textbook on chaos; class-tested, elementary but rigorous, with applications and lots of pictures and exercises.

John Banks (Author), Valentina Dragan (Author), Arthur Jones (Author)

9780521531047, Cambridge University Press

Paperback, published 8 May 2003

306 pages, 154 b/w illus. 303 exercises
22.8 x 15.2 x 1.8 cm, 0.453 kg

'… presented in such a form that it is accessible to anyone who has taken an undergraduate calculus course … This textbook is highly recommended for a one semester undergraduate introduction to chaos theory.' Acta Sci. Math.

When new ideas like chaos first move into the mathematical limelight, the early textbooks tend to be very difficult. The concepts are new and it takes time to find ways to present them in a form digestible to the average student. This process may take a generation, but eventually, what originally seemed far too advanced for all but the most mathematically sophisticated becomes accessible to a much wider readership. This book takes some major steps along that path of generational change. It presents ideas about chaos in discrete time dynamics in a form where they should be accessible to anyone who has taken a first course in undergraduate calculus. More remarkably, it manages to do so without discarding a commitment to mathematical substance and rigour. The book evolved from a very popular one-semester middle level undergraduate course over a period of several years and has therefore been well class-tested.

Preface
1. Making predictions
2. Mappings and orbits
3. Periodic orbits
4. Asymptotic orbits I: linear and affine mappings
5. Asymptotic orbits II: differentiable mappings
6. Families of mappings and bifurcations
7. Graphical composition, wiggly iterates and zeros
8. Sensitive dependence
9. Ingredients of chaos
10. Schwarzian derivatives and 'woggles'
11. Changing coordinates
12. Conjugacy
13. Wiggly iterates, Cantor sets and chaos
Index.

Subject Areas: Chaos theory [PBWS]