Mathematical Tools for One Dimensional Dynamics 1st Edition by Edson De Faria, Welington De Melo ISBN 0511438613 9780521888615

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Product details:

ISBN 10: 0511438613

ISBN 13: 9780521888615 

Author: Edson De Faria, Welington De Melo

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.

• Includes complete proofs of major tools used in real and complex one-dimensional dynamics, some of which have never before appeared in book format
• Numerous exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics
• Appendix on Riemann surfaces and Teichmüller theory includes proofs of some key results in this theory, such as the Bers embedding

Table of contents:

Preface
1. Introduction
2. Preliminaries in complex analysis
3. Uniformization and conformal distortion
4. The measurable Riemann mapping theorem
5. Holomorphic motions
6. The Schwarzian derivative and cross-ratio distortion
7. Appendix: Riemann Surfaces and Teichmüller spaces
Bibliography
Index.

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Tags: Edson De Faria, Welington De Melo, Mathematical, Tools, One Dimensional, Dynamics