Functional Equations related to the
Iteration of Functions

by Ron Resch, South Fallsburg, NY
Frank Stenger, University of Utah, Salt Lake City and
Jörg Waldvogel, Swiss Federal Institute of Technology ETH,
CH-8092 Zürich, Switzerland


Certain systems of functional equations related to the iteration of functions with a fixed point are considered. We construct smooth solutions in terms of expansions about a fixed point. In a particular example taken from an intuitive geometric situation the solution is obtained explicitly as a convergent Taylor series. Particular attention is given to the question of selecting distinguished solutions from a continuum of possible solutions. This classical topic is presented in a transparent way by consistently using compositional notation. The method described may be applied in similar situations, e.g. for handling iterations arising in discrete dynamical systems.

Download the complete paper (15 pages), appeared in Aequationes Math. 60, 2000, 25-37: functequ.pdf