Accumulation points of iterated function systems

The sequence {Fn} is called the iterated function system corresponding to {fn}. For readability, we denote by F(Ω, X) the set of all iterated function systems made from functions in Hol(Ω, X). By Montel’s theorem (see for example [2]), the sequence Fn is a normal family, and every convergent subsequence converges uniformly on compact subsets of Ω to a holomorphic function F ∈ Hol(Ω, X). The accumulation functions F are called accumulation points of the IFS and are either open or constant maps. The constant accumulation points may be located either inside X or on the boundary of X. Whether there are non-constant accumulation points and whether accumulation points may take values on the boundary of X depends on the geometry of X. In [1], the authors introduced the concept of a Bloch subdomain as follows: