Semigroups of transcendental entire functions and their dynamics
Dynamical Systems
2015-10-08 v5
Abstract
We study the dynamics of an arbitrary semigroup of transcendental entire functions using Fatou-Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroups. We provide some conditions for connectivity of the Julia set of the transcendental semigroups. We also study finitely generated transcendental semigroups, abelian transcendental semigroups and limit functions of transcendental semigroups on its invariant Fatou components.
Keywords
Cite
@article{arxiv.1405.0224,
title = {Semigroups of transcendental entire functions and their dynamics},
author = {Dinesh Kumar and Sanjay Kumar},
journal= {arXiv preprint arXiv:1405.0224},
year = {2015}
}
Comments
12 pages, accepted for publication in Proc. Indian Acad. Sci. (Math. Sci.). arXiv admin note: text overlap with arXiv:1302.7249