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 …

Let f be a transcendental entire function and let A (f) denote the set of points that escape to
infinity 'as fast as possible'under iteration. By writing A (f) as a countable union of closed …

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 prove an analog of Böttcher's theorem for transcendental entire functions in the
Eremenko–Lyubich class $\mathcal {B} $. More precisely, let f and g be entire functions with …

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 dynamical behaviour of a transcendental entire function in any periodic component of
the Fatou set is well understood. Here we study the dynamical behaviour of a transcendental …

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 …

Let f be a transcendental entire function of finite order in the Eremenko–Lyubich class B (or a
finite composition of such maps), and suppose that f is hyperbolic and has a unique Fatou …

A hyperbolic transcendental entire function with connected Fatou set is said to be" of disjoint
type". It is known that a disjoint-type function provides a model for the dynamics near infinity …