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 …

We show that an invariant Fatou component of a hyperbolic transcendental entire function is
a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points …

Abstract The Douady-Hubbard landing theorem for periodic external rays is one of the
cornerstones of the study of polynomial dynamics. It states that, for a complex polynomial f …

If is in the Eremenko–Lyubich class (transcendental entire functions with bounded singular
set), then and must satisfy certain simple topological conditions when is sufficiently large. A …

For polynomials, local connectivity of Julia sets is a much‐studied and important property.
Indeed, when the Julia set of a polynomial of degree d⩾ 2 d\geqslant2 is locally connected …

Abstract The Eremenko–Lyubich class B consists of transcendental entire functions with
bounded singular set and the Speiser class S⊂ B is made up of functions with a finite …

It is known that, for many transcendental entire functions in the Eremenko-Lyubich class
$\mathcal {B} $, every escaping point can eventually be connected to infinity by a curve of …

Abstract for any δ> 0 we construct an entire function f with three singular values whose Julia
set has Hausdorff dimension at most 1+ δ. Stallard proved that the dimension must be strictly …

In recent years, there has been significant progress in the understanding of the dynamics of
transcendental entire functions with bounded postsingular set. In particular, for certain …

Much recent work on the iterates of a transcendental entire function $ f $ has been motivated
by Eremenko's conjecture that all the components of the escaping set $ I (f) $ are …