Escaping set and Bounded Orbit Set of Holomorphic Semigroup on C

Abstract

In this paper, we study the structure and properties of escaping sets of holomorphic semigroups. In particular, we study the relationship between escaping set of holomorphic semigroup and escaping set of each function that lies in that semigroup. We also study about the invariantness of escaping sets. Also, in this paper, we define the term bounded orbit set K(H) and the set K'(H) of holomorphic semigroup H. Then we study their invariantness and their relations with escaping sets. We also construct a particular class of holomorphic semigroups generated by two holomorphic functions such that bounded orbit set of holomorphic semigroup is equal to bounded orbit set of its generators.