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

Authors: BISHNU HARI SUBEDI, AJAYA SINGH

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

Full Text: PDF