Open AccessFatou, Julia, and escaping sets in holomorphic (sub)semigroup dynamics
Author(s) -
Bishnu Hari Subedi,
Ajaya Kumar Singh
Publication year - 2019
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1810-133
Subject(s) - julia set , holomorphic function , mathematics , semigroup , transcendental number , pure mathematics , discrete mathematics , mathematical analysis
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.
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