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 …

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 …

Recently, Bishop constructed the first example of a bounded‐type transcendental entire
function with a wandering domain using a new technique called quasiconformal folding. It is …

In 1988, Mayer proved the remarkable fact that ∞∞ is an explosion point for the set E (f_a) E
(fa) of endpoints of the Julia set of f_a: C → C; e^ z+ a fa: C→ C; ez+ a with a<-1 a<-1; that is …

We show that there exists a hyperbolic entire function f of finite order of growth such that the
hyperbolic dimension, that is, the Hausdorff dimension of the set of points in the Julia set of f …

We investigate some connectedness properties of the set of points K (f) where the iterates of
an entire function f are bounded. We describe a class of transcendental entire functions for …

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 …

We study the dynamics of a collection of families of transcendental entire functions which
generalizes the well-known exponential and cosine families. We show that, for functions in …

We study the dynamical behaviour of points in the boundaries of simply connected invariant
Baker domains U of meromorphic maps f with a finite degree on U. We prove that if f| U is of …

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 …