We investigate under what conditions the Fatou, Julia, and escaping sets of a transcendental semigroup are respectively equal to the Fatou, Julia, and escaping sets of their subsemigroups. We define the partial fundamental set and fundamental set of a holomorphic semigroup, and on the basis of these sets, we prove that the Fatou and escaping sets of a transcendental semigroup $ S $ are nonempty.
SUBEDI, BISHNU HARI and SINGH, AJAYA
"Fatou, Julia, and escaping sets in holomorphic (sub)semigroup dynamics,"
Turkish Journal of Mathematics: Vol. 43:
2, Article 25.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss2/25