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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Dynamics in the Eremenko-Lyubich class
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by David J. Sixsmith PDF
Conform. Geom. Dyn. 22 (2018), 185-224 Request permission


The study of the dynamics of polynomials is now a major field of research, with many important and elegant results. The study of entire functions that are not polynomials – in other words transcendental entire functions – is somewhat less advanced, in part due to certain technical differences compared to polynomial or rational dynamics.

In this paper we survey the dynamics of functions in the Eremenko-Lyubich class, $\mathcal {B}$. Among transcendental entire functions, those in this class have properties that make their dynamics most “similar” to the dynamics of a polynomial, and so particularly accessible to detailed study. Many authors have worked in this field, and the dynamics of class $\mathcal {B}$ functions is now particularly well-understood and well-developed. There are many striking and unexpected results. Several powerful tools and techniques have been developed to help progress this work. There is also an increasing expectation that learning new results in transcendental dynamics will lead to a better understanding of the polynomial and rational cases.

We consider the fundamentals of this field, review some of the most important results, techniques and ideas, and give stepping-stones to deeper inquiry.

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Additional Information
  • David J. Sixsmith
  • Affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom. ORCiD: 0000-0002-3543-6969
  • MR Author ID: 952973
  • Email:
  • Received by editor(s): June 11, 2018
  • Received by editor(s) in revised form: July 26, 2018
  • Published electronically: September 11, 2018
  • © Copyright 2018 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 22 (2018), 185-224
  • MSC (2010): Primary 37F10; Secondary 30D05
  • DOI:
  • MathSciNet review: 3852466