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

Authors : Bishnu Hari SUBEDI, Ajaya SINGH

Pages : 930-940

View : 18 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

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