This volume studies the dynamics of iterated holomorphic mappings from a Riemann
surface to itself, concentrating on the classical case of rational maps of the Riemann sphere …

The points which converge to∞ under iteration of the maps z↦ λ (z) for λ∈ C/{0} are
investigated. A complete classification of such 'escaping points' is given: they are organized …

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 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 …

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 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 thesis contains several new results about the dynamics of exponential maps $
z\mapsto\exp (z)+\kappa $. In particular, we prove that periodic external rays of exponential …

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 …