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 construct a non-polynomial entire function whose Julia set has finite 1-dimensional
spherical measure, and hence Hausdorff dimension 1. In 1975, Baker proved the dimension …

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 …

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 …

We prove density of hyperbolicity in spaces of (i) real transcendental entire functions,
bounded on the real line, whose singular set is finite and real and (ii) transcendental …

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 …

Inou and Shishikura provided a class of maps that is invariant by near-parabolic
renormalization, and that has proved extremely useful in the study of the dynamics of …

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 …

In this paper, we develop Pesin theory for the boundary map of some Fatou components of
transcendental functions, under certain hyptothesis on the singular values and the Lyapunov …

A generalized family of transcendental (non-polynomial entire) functions is constructed,
where the Hausdorff dimension and the packing dimension of the Julia sets are equal to …