- Turkish Journal of Mathematics
- Vol: 43 Issue: 2
- Fatou, Julia, and escaping sets in holomorphic (sub)semigroup dynamics
Fatou, Julia, and escaping sets in holomorphic (sub)semigroup dynamics
Authors : Bishnu Hari Subedi, Ajaya Singh
Pages : 930-940
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :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.Keywords : Transcendental semigroup, escaping set, finite index, cofinite index, Rees index, partial fundamental set, fundamental set