Mathematical Tools for One-Dimensional Dynamics

ISBN-13: 9780521888615 / Angielski / Twarda / 2008 / 208 str.

Edson De Faria; Edson De Faria; Welington De Melo

Opis

Detailing the very latest research, 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. Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. This necessary 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.

Recenzje

'… 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

Spis treści

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.