ABSTRACT

For a transcendental entire or meromorphic function f, this chapter focuses on the behavior of the components of the Fatou set F(f) and the behavior of f on its Fatou set. It shows that there are some essential differences among rational functions, transcendental entire functions and transcendental meromorphic functions. The chapter examines nonconstant limit functions and the growth of the function in its stable domains, especially in Baker domain. It shows that there are no Baker domains for some functions. Wandering components of the Fatou set are called as wandering domains. By Sullivan’s theorem, there is no wandering domain for any nonlinear rational function. But for transcendental functions, the cases are very different. The chapter discusses the three classes: functions for the class E, functions for the class M, and functions without wandering domains.