1. INTRODUCTION. The concept of dimension has many aspects and meanings within
mathematics, and there are a number of very different definitions of what the dimension of a …

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 …

For the family of exponential maps are conjugate on suitable subsets of their escaping sets,
and this conjugacy is quasiconformal. Furthermore, we prove that any two attracting and …

We give a topological characterization of postsingularly finite topological exponential maps,
ie, universal covers $ g\colon\mathbb {C}\to\mathbb {C}\setminus\{0\} $ such that $0 $ has a …

This article investigates the parameter space of the exponential family z↦\exp(z)+κ. We
prove that the boundary (in ℂ) of every hyperbolic component is a Jordan arc, as …

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 study the dynamics of iterated cosine maps $ E\colon z\mapsto ae^ z+ be^{-z}, $ with $
a, b\in\C\setminus\{0\} $. We show that the points which converge to infinity under iteration …

We consider the case of an exponential map for which the singular value is accessible from
the set of escaping points. We show that there are dynamic rays of which do not land. In …

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 investigate the set I of parameters κ∈ ℂ for which the singular orbit (0, eκ,…) of Eκ (z):=
exp (z+ κ) converges to. These parameters are organized in curves in parameter space …