Mathematical Tools for One-Dimensional Dynamics

Edson de Faria; Welington de Melo

doi:10.1017/CBO9780511755231

Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This self-contained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the Bers-Royden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmüller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics.

'… a successful self-contained exposition of an important part of the theory with indications for further studies and discussion of perspectives, including fundamental open problems.'

Source: EMS Newsletter

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Mathematical Tools for One-Dimensional Dynamics

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - Introduction
pp 1-5

2 - Preliminaries in complex analysis
pp 6-17

3 - Uniformization and conformal distortion
pp 18-77

4 - The measurable Riemann mapping theorem
pp 78-122

5 - Holomorphic motions
pp 123-154

6 - The Schwarzian derivative and cross-ratio distortion
pp 155-167

Appendix: Riemann surfaces and Teichmüller spaces
pp 168-184

References
pp 185-189

Index
pp 190-191

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