Cover image for Chaos : a mathematical introduction
Title:
Chaos : a mathematical introduction
Author:
Banks, John, 1957-
Personal Author:
Publication Information:
Cambridge ; New York : Cambridge University Press, [2003]

©2003
Physical Description:
xi, 294 pages : illustrations ; 23 cm.
Language:
English
ISBN:
9780521531047
Format :
Book

Available:*

Library
Call Number
Material Type
Home Location
Status
Central Library QA614.8 .B36 2003 Adult Non-Fiction Non-Fiction Area
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Summary

Summary

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.


Table of Contents

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

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