A new characterisation of the Eremenko-Lyubich class
D. J. Sixsmith
TL;DR
This paper introduces a novel characterization of the Eremenko-Lyubich class of transcendental entire functions, enhancing understanding of their singularities and providing new insights into their structure.
Contribution
It offers a new characterization of the Eremenko-Lyubich class and presents a novel result on non-logarithmic direct singularities.
Findings
New characterization of the Eremenko-Lyubich class
Results on direct singularities that are not logarithmic
Enhanced understanding of singular value structures
Abstract
The Eremenko-Lyubich class of transcendental entire functions with a bounded set of singular values has been much studied. We give a new characterisation of this class of functions. We also give a new result regarding direct singularities which are not logarithmic.
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Taxonomy
TopicsMeromorphic and Entire Functions · Mathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems