  In this paper, we prove that escaping set of transcendental semigroup is
S-forward invariant. We also prove that if holomorphic semigroup is abelian,
then Fatou set, Julia set and escaping set are S-completely invariant. We see
certain cases and conditions that the holomorphic semigroup dynamics exhibits
same dynamical behavior just like the classical complex dynamics. Frequently,
we also examine certain amount of connection and contrast between classical
complex dynamics and holomorphic semigroup dynamics.
