Chaos A Mathematical Introduction

Here is a textbook that 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. Remarkably, it manages to do so without discarding a commitment to mathematical substance and rigour. The book has evolved from a very popular one-semester middle level undergraduate course and has therefore been well class-tested. It includes a number of innovative features and is the first elementary presentation of what is traditionally an advanced subject. Key Features: -The first presentation of the subject at such an accessible level -An easy pace of development, with graded exercises in each section, and a wealth of explanatory graphs and diagrams -Thoroughly class-tested 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.