Cyclic Phenomena for Composition Operators, Numéro 596

The cyclic behaviour of a composition operator is closely tied to the dynamical behaviour of its inducing map. Based on analysis of fixed-point and orbital properties of inducing maps, Bourdon and Shapiro show that composition operators exhibit strikingly diverse types of cyclic behaviour. The authors connect this behaviour with classical problems involving polynomial approximation and analytic functional equations. This pioneering work forges new links between classical function theory and operator theory, and contributes new results to the study of classical analytic functional equations.