**Memoirs of the American Mathematical Society**

1997;
105 pp;
Softcover

MSC: Primary 47;
Secondary 30

Print ISBN: 978-0-8218-0630-2

Product Code: MEMO/125/596

List Price: $47.00

Individual Member Price: $28.20

**Electronic ISBN: 978-1-4704-0181-8
Product Code: MEMO/125/596.E**

List Price: $47.00

Individual Member Price: $28.20

# Cyclic Phenomena for Composition Operators

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*Paul S. Bourdon; Joel H. Shapiro*

The cyclic behavior of a composition operator is closely tied
to the dynamical behavior 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 behavior. The authors connect this behavior with
classical problems involving polynomial approximation and analytic
functional equations.

Features:

- Complete classification of the cyclic behavior of composition operators induced by linear-fractional mappings.
- Application of linear-fractional models to obtain more general cyclicity results.
- Information concerning the properties of solutions to Schroeder's and Abel's 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.

#### Readership

Graduate students and research mathematicians interested in complex analysis and its interaction with operator theory.