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.
On proper analytic maps with one critical point by W. Bergweiler Non-Archimedean analytic maps to algebraic curves by W. Cherry and J. T.-Y. Wang Some progress in non-Archimedean analysis by P.-C. Hu and C.-C. Yang On period doubling phenomena and Sharkovskii type ordering for the family $\lambda\tan(z)$ by L. Keen and J. Kotus The parabolic implosion: Lavaurs maps and strong convergence for rational maps by R. Oudkerk Synthetic deformation space of an entire function by M. Taniguchi.