Memoirs of the American Mathematical Society 1997; 105 pp; softcover Volume: 125 ISBN10: 0821806300 ISBN13: 9780821806302 List Price: US$47 Individual Members: US$28.20 Institutional Members: US$37.60 Order Code: MEMO/125/596
 The cyclic behavior of a composition operator is closely tied to the dynamical behavior of its inducing map. Based on analysis of fixedpoint 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 linearfractional mappings.
 Application of linearfractional 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. Table of Contents  Introduction
 Preliminaries
 Linearfractional composition operators
 Linearfractional models
 The hyperbolic and parabolic models
 Cyclicity: Parabolic nonautomorphism case
 Endnotes
 References
