Chaos: A Mathematical Introduction

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John Banks (La Trobe University, Victoria) Valentina Dragan (La Trobe University, Victoria)

Chaos

A Mathematical Introduction

John Banks (La Trobe University, Victoria), Valentina Dragan (La Trobe University, Victoria), Arthur Jones (La Trobe University, Victoria)

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English

Cambridge University Press
24 July 2003

Mathematics & Sciences; Chaos theory

Series: Australian Mathematical Society Lecture Series

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.

By: John Banks (La Trobe University Victoria), Valentina Dragan (La Trobe University, Victoria), Arthur Jones (La Trobe University, Victoria)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: No. 18
Dimensions: Height: 228mm, Width: 152mm, Spine: 18mm
Weight: 453g
ISBN: 9780521531047
ISBN 10: 0521531047
Series: Australian Mathematical Society Lecture Series
Pages: 306
Publication Date: 24 July 2003
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Reviews for Chaos: A Mathematical Introduction

'The tone, pace and level of the book are nicely judged for middle level undergraduates studying mathematics. The authors' friendly style, and the fact that the material has been developed from taught courses make the book ideal for self-study, and as a prelude to reading extensive treatments of chaos theory.' The Mathematical Gazette '... 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.