Holomorphic Dynamics on Hyperbolic Riemann Surfaces

✍ Scribed by Marco Abate

• Publisher: De Gruyter
• Year: 2022
• Tongue: English
• Leaves: 372
• Series: De Gruyter Studies in Mathematics; 89
• Category: Library

✦ Synopsis

This completely revised and updated edition of the one variable part of the author's classic older book "Iteration Theory of Holomorphic Maps on Taut Manifolds" presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a reference book for the experts and as an accessible gateway to this beautiful theory for Master and Ph.D. students. It also contains extensive historical notes and references for further readings.

• A revised and updated edition of a classic book in complex dynamics
• Written by one of the foremost experts in the field
• Of interest to graduate students and researhers in holomorphic dynamics, complex geometry, and geometric function theory

✦ Table of Contents

Contents
Introduction
1 The Schwarz lemma and Riemann surfaces
2 Boundary Schwarz lemmas
3 Discrete dynamics on Riemann surfaces
4 Discrete dynamics on the unit disk
5 Continuous dynamics on Riemann surfaces
A Appendix
Bibliography
Index