This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental case is analogous to the rational case are treated rather briefly here. For example, we introduce the different types of components of the Fatou set that occur in the iteration of rational functions but omit a detailed description of these types. Instead, we concentrate on the types of components that are special to transcendental functions (Baker domains and wandering domains).

/pdf/iteration-of-meromorphic-functions-5an8yxam4g.pdf

Lectures on the general theory of integral functions

Iteration of meromorphic functions

Suppose that 1.1 is a transcendental integral function. In this article we develop the theory initiated by Wiman [22, 23] and deepened by other writers including Valiron [18, 19, 20], Saxer [15], Clunie [4, 5] and Kovari [10, 11], which describes the local behaviour of f(z), near a point where | f(z) | is large, in terms of the power seriesf of f(z).

background

/pdf/the-local-growth-of-power-series-a-survey-of-the-wiman-2e3o0gy9xf.pdf

The Local Growth of Power Series: A Survey of the Wiman-Valiron Method

Characteristics of the behavior of a meromorphic function and the first fundamental theorem Meromorphic functions of finite order The second fundamental theorem Deficient values Asymptotic properties of meromorphic functions and deficiencies Value distribution with respect to the arguments Applications of Riemann surfaces to value distribution On the magnitude of an entire function Notes A survey of some results after 1970 Bibliography References added to the English edition Author index Subject index Notation index.

Value Distribution of Meromorphic Functions

On considere l'equation differentielle f''+A(z)f'+B(z) f=0 ou A(z) et B(z) sont des fonctions entieres. On trouve des conditions sur A(z) et B(z) qui garantissent que chaque solution f¬=0 de l'equation a un ordre fini

methods

/pdf/finite-order-solutions-of-second-order-linear-differential-12vico8puz.pdf

Finite order solutions of second order linear differential equations

Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = ?f(z) = f(z + 1) - f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f. The results may be viewed as discrete analogues of existing theorems on the zeros of f' and f'/f.

Lectures on the general theory of integral functions

Citations

Iteration of meromorphic functions

The Local Growth of Power Series: A Survey of the Wiman-Valiron Method

Value Distribution of Meromorphic Functions

Finite order solutions of second order linear differential equations

Zeros of differences of meromorphic functions

Related Papers (5)

The Local Growth of Power Series: A Survey of the Wiman-Valiron Method

Nevanlinna Theory and Complex Differential Equations

Estimates for the Logarithmic Derivative of a Meromorphic Function, Plus Similar Estimates

Uniqueness Theory of Meromorphic Functions

Neuere Untersuchungen über eindeutige analytische Funktionen