Unbounded Fatou components of composite transcendental meromorphic functions with finitely many poles - Maneeruk K. (2014)
Let fi, i = 1, 2,..., m be transcendental meromorphic functions of order less than 1 2 with at most finitely many poles and at least one of them has positive lower order. Let g = fm {ring operator} fm-1 {ring operator}. . .{ring operator} f1. Then either g has no unbounded Fatou components or at least one unbounded Fatou component g is multiply connected.