Abstract

In order to introduce the dynamics of the class of transcendental meromorphic functions with at least one pole which is not omitted, denoted by \(\mathscr {M}\), we introduce the class Mer. The main definitions and properties concerning the Stable and Chaotic sets of functions in class Mer are presented. We define the escaping set, of a function in class Mer, which is useful to program the computer in order to get dynamical planes for some functions in three families given in Sect. 8.4. We also explain some dynamical differences between classes of functions contained in Mer.

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