Dynamics in the Eremenko-Lyubich class

Available on the arXiv.

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