We construct an entire function in the Eremenko-Lyubich class [symbol] whose Julia set has
only bounded path-components. This answers a question of Eremenko from 1989 in the …

1. INTRODUCTION. The concept of dimension has many aspects and meanings within
mathematics, and there are a number of very different definitions of what the dimension of a …

Let $ f $ be a transcendental entire function and let $ I (f) $ be the set of points whose
iterates under $ f $ tend to infinity. We show that $ I (f) $ has at least one unbounded …

Let f be a transcendental meromorphic function and denote by J (f) the Julia set and by I (f)
the escaping set. We show that if f has a direct singularity over infinity, then I (f) has an …

Complex dynamics of iterated entire holomorphic functions is an active and exciting area of
research. This manuscript collects known background in this field and describes several of …

We develop a general technique for realising full closed subsets of the complex plane as
wandering sets of entire functions. Using this construction, we solve a number of open …

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 …

For a transcendental entire function f, we study the set of points BU (f) whose iterates under f
neither escape to infinity nor are bounded. We give new results on the connectedness …

Let f be an entire transcendental map of finite order, such that all the singularities of f− 1 are
contained in a compact subset of the immediate basin B of an attracting fixed point. It is …

For the family of exponential maps are conjugate on suitable subsets of their escaping sets,
and this conjugacy is quasiconformal. Furthermore, we prove that any two attracting and …