Bishnu Hari SUBEDI, Ajaya SINGH

100110

Fatou, Julia, and escaping sets in holomorphic (sub)semigroup dynamics

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,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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