We prove an analog of Böttcher's theorem for transcendental entire functions in the
Eremenko–Lyubich class $\mathcal {B} $. More precisely, let f and g be entire functions with …

We show that for any transcendental meromorphic function $ f $ there is a point $ z $ in the
Julia set of $ f $ such that the iterates $ f^ n (z) $ escape, that is, tend to $\infty $, arbitrarily …

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 show that an invariant Fatou component of a hyperbolic transcendental entire function is
a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points …

We study the post-critical set of a class of holomorphic systems with an irrationally indifferent
fixed point. We prove a trichotomy for the topology of the post-critical set based on the …

Let f be a transcendental entire function of finite order in the Eremenko–Lyubich class B (or a
finite composition of such maps), and suppose that f is hyperbolic and has a unique Fatou …

We discuss in detail the dynamics of maps z↦ ae z+ be-z for which both critical orbits are
strictly preperiodic. The points that converge to∞ under iteration contain a set R consisting …

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 …

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 …