Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1810-133
Keywords
Transcendental semigroup, escaping set, finite index, cofinite index, Rees index, partial fundamental set, fundamental set
First Page
930
Last Page
940
Recommended Citation
SUBEDI, B. H, & SINGH, A (2019). Fatou, Julia, and escaping sets in holomorphic (sub)semigroup dynamics. Turkish Journal of Mathematics 43 (2): 930-940. https://doi.org/10.3906/mat-1810-133
