Continuous one-parameter semigroups of holomorphic self-maps of the unit disc D in the
complex plane C have been a subject of study since early 1900s, both for their intrinsic …

Linearization models for discrete and continuous time dynamical systems are the driving
forces for modern geometric function theory and composition operator theory on function …

Abstract The Schwarz Lemma has given impetus to developments in several areas of
complex analysis and mathematics in general. We survey some investigations related to its …

We obtain a generalization of the Burns-Krantz rigidity theorem for holomorphic self-
mappings of the unit disk in the spirit of the classical Schwarz-Pick Lemma and its …

We study linearization models for continuous one-parameter semigroups of parabolic type.
In particular, we introduce new limit schemes to obtain solutions of Abel's functional …

For holomorphic selfmaps of the open unit disc $\U $ that are not elliptic automorphisms, the
Schwarz Lemma and the Denjoy-Wolff Theorem combine to yield a remarkable result: each …

The embeddability problem is a very old and hard problem in discrete holomorphic iteration
which deals with determining general conditions on a given univalent self-map $\varphi $ of …

The goal of this paper is twofold. First, to give purely local boundary uniqueness results for
maps defined only on one side as germs at a boundary point and hence not necessarily …

We prove the existence and the essential uniqueness of canonical models for the forward
(resp., backward) iteration of a holomorphic self-map f of a cocompact Kobayashi hyperbolic …

This equation has a solution if, for instance,| f (0)|< 1 (see Königs [16]). In particular, if f∈ Hol
(,) is a self-map (not an automorphism) of the unit disc⊂ C, then there exists a solution σ of …