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Fatou, Julia, And Escaping Sets In Holomorphic (Sub)Semigroup Dynamics, Bishnu Hari Subedi, Ajaya Singh

Turkish Journal of Mathematics

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.