**Contemporary Mathematics**

Volume: 303;
2002;
136 pp;
Softcover

MSC: Primary 11; 30; 32; 37;

Print ISBN: 978-0-8218-2980-6

Product Code: CONM/303

List Price: $48.00

Individual Member Price: $38.40

**Electronic ISBN: 978-0-8218-7893-4
Product Code: CONM/303.E**

List Price: $48.00

Individual Member Price: $38.40

# Value Distribution Theory and Complex Dynamics

Share this page *Edited by *
*William Cherry; Chung-Chun Yang*

This volume contains six detailed papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. It demonstrates the strong interconnections between the two fields and introduces recent progress of leading researchers from Asia.

In the book, W. Bergweiler discusses proper analytic maps with one critical point and generalizes a previous result concerning Leau domains. W. Cherry and J. Wang discuss non-Archimedean analogs of Picard's theorems. P.-C. Hu and C.-C. Yang give a survey of results in non-Archimedean value distribution theory related to unique range sets, the \(abc\)-conjecture, and Shiffman's conjecture. L. Keen and J. Kotus explore the dynamics of the family of \(f_\lambda(z)=\lambda\tan(z)\) and show that it has much in common with the dynamics of the familiar quadratic family \(f_c(z)=z^2+c\). R. Oudkerk discusses the interesting phenomenon known as parabolic implosion and, in particular, shows the persistence of Fatou coordinates under perturbation. Finally, M. Taniguchi discusses deformation spaces of entire functions and their combinatorial structure of singularities of the functions.

The book is intended for graduate students and research mathematicians interested in complex dynamics, function theory, and non-Archimedean function theory.

#### Table of Contents

# Table of Contents

## Value Distribution Theory and Complex Dynamics

- Contents v6 free
- Preface vii8 free
- On proper analytic maps with one critical point 110 free
- Non-Archimedean analytic maps to algebraic curves 716
- Some progress in non-Archimedean analysis 3746
- On period doubling phenomena and Sharkovskii type ordering for the family λ tan(z) 5160
- The parabolic implosion: Lavaurs maps and strong convergence for rational maps 7988
- Synthetic deformation space of an entire function 107116

#### Readership

Graduate students and research mathematicians interested in complex dynamics, function theory, and non-Archimedean function theory.