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Functional Equations Related to the Iteration of Functions

by R. Resch and F. Stenger and J. Waldvogel

(Report number 1996-14)

Abstract
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 the 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 an infinity 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.

Keywords:

@Techreport{RSW96_197,
  author = {R. Resch and F. Stenger and J. Waldvogel},
  title = {Functional Equations Related to the Iteration of Functions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-14.pdf },
  year = {1996}
}

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