De Faria E., de Melo W. Mathematical Tools for One-Dimensional Dynamics

Cambridge University Press, UK, 2008. — 201 p. — Cambridge Studies in Advanced Mathematics 115) — ISBN: 0521888611.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.Preliminaries in complex analysis
Uniformization and conformal distortion
The measurable Riemann mapping theorem
Holomorphic motions
The Schwarzian derivative and cross-ratio distortion
Appendix. Riemann surfaces and Teichm¨uller spaces