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 study the boundary behaviour of a meromorphic map $ f:\mathbb {C}\to\widehat
{\mathbb {C}} $ on its simply connected invariant Fatou component $ U $. To this aim, we …

We study the behaviour of a transcendental entire map $ f\colon\mathbb {C}\to\mathbb {C} $
on an unbounded invariant Fatou component $ U $, assuming that infinity is accessible from …

Hyperbolicity plays an important role in the study of dynamical systems, and is a key concept
in the iteration of rational functions of one complex variable. Hyperbolic systems have also …

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 …

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 …

Let f be a transcendental entire function, and let U, V ⊂ CU, V⊂ C be disjoint simply-
connected domains. Must one of f^-1 (U) f-1 (U) and f^-1 (V) f-1 (V) be disconnected? In …

Let f be a function in the Eremenko-Lyubich class B, and let U be an unbounded, forward
invariant Fatou component of f. We relate the number of singularities of an inner function …

Suppose that f is a transcendental entire function, VCV⊊ C is a simply connected domain,
and U is a connected component of f^-1 (V) f-1 (V). Using Riemann maps, we associate the …