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.
Transcendental semigroup, escaping set, finite index, cofinite index, Rees index, partial fundamental set, fundamental set
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