For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna 188] himself proved that for two nonconstant meromorphic func tions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai)...

This book gives a comprehensive and up-to-date survey on dynamics and related topics, such as Fatou-Julia type theory, the Ergodic theorem and invariant sets, hyperbolicity in differentiable or complex dynamics, iterant ion theory on Pm, complex dynamics in Cm and the foundations of differentiable and complex dynamics. The main aims of this volume are, firstly, to advance the study of the above-named topics and to establish the corresponding Fatou-Julia results for complex manifolds, and, secondly, to provide some advanced account of dynamical systems within the framework of geometry and...

This book introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Secondly, it gives applications of the above theory to, e.g., abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new...