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 …

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 complete classification of the set of parameters $\kappa $ for which the singular
value of $ E_ {\kappa}: z\mapsto\exp (z)+\kappa $ escapes to $\infty $ under iteration. In …

We investigate the dynamics of exponential maps z↦→ λez; the goal is a description by
means of dynamic rays. We discuss landing properties of dynamic rays and show that in …

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 …

Let f be an entire function whose set of singular values is bounded and suppose that f has a
Siegel disk U such that f|∂ U is a homeomorphism. We show that U is bounded. Using a …

We study the parameter planes of certain one-dimensional, dynamically-defined slices of
holomorphic families of entire and meromorphic transcendental maps of finite type. Our …

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 …