Mathematical Tools for One-Dimensional Dynamics

Presents the major mathematical tools necessary for the study of complex dynamics.

Edson de Faria (Author), Welington de Melo (Author)

9780521888615, Cambridge University Press

Hardback, published 2 October 2008

208 pages, 56 exercises
23.3 x 15.5 x 1.5 cm, 0.41 kg

'… 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.' EMS Newsletter

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.

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.

Subject Areas: Nonlinear science [PBWR], Numerical analysis [PBKS]