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arXiv · 1405.0224

Semigroups of transcendental entire functions and their dynamics

Dinesh Kumar·Sanjay Kumar
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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.

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Dinesh Kumar, Sanjay Kumar. 2014-05-01. Semigroups of transcendental entire functions and their dynamics. https://arxiv.org/abs/1405.0224

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