2004•Journal of Tsinghua University(Science and Technology)Requires access

Connectivity of Julia sets of transcendental semigroups

Zhigang Huang

Abstract

This paper analyzes the dynamic properties of semigroups generated by a family of transcendental entire functions with the semigroup operation being functional composition. Fatou-Julia theory was used to investigate the connectivity of the Julia set of these semigroups as a subset of the complex plane. Conditions were defined to connect the Julia set of the semigroup. After adding a point representing infinity to the Julia set, two sufficient conditions were specified for the Julia set to be connected as a subset of a Riemann sphere.

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Key concepts: Julia set, Mathematics, Riemann sphere, Semigroup, Transcendental number, Newton fractal, Special classes of semigroups, Entire function