Two Types Of Power System, Transcendental Functions

The exponential maps Aexp(z) may be regarded as the simplest class of tran-scendental entire function, and the maps in sine family λsin z exhibits the typical dynamical properties of both exponential and quadratic maps. Their dynamics have been extensively studied and quite well understood by several authors. In this thesis, we mainly study the dynamics of F(z)=exp(z)/z on the punctured complex plane C*=C\{0}, which belongs to a class of transcendental meromorphic functions with exactly one pole which is a Picard-exceptional value, and the dynamics of sine family λsin z on the parameter plane. This thesis is divided into four chapters.In Chapter1, we give some usual notations, definitions and preliminary knowl-edge.In Chapter2, we study the dynamics of F on C*and show that F is not recurrent.In Chapter3, we consider the escaping set of F and prove that it has Hausdorff dimension two.In Chapter4, we investigate the dynamics of the sine family on the parameter plane and obtain that the set of non-escaping parameters of the sine family has finite area in any vertical strip of finite width.