Progress of iteration theory since 1981
type: Item
instance of: scholarly article
title: Progress of iteration theory since 1981
zbMATH Open document ID: 0860.39029
DOI: 10.1007/BF01831113
author: Gy. Targoński
published in: Aequationes Mathematicae
publication date: 1997-04-28T00:00:00Z
full work available at URL: https://eudml.org/doc/137620
review text: In this survey the author tries to highlight a number of recent developments in iteration theory, and to point out a number of unsolved problems, thus also trying to predict the direction the evolution may take. The following fields within iteration theory are treated: orbit theory, algebraic iteration theory, iteration of formal power series, Liedl's Pilgerschritt transformation, the Aczél-Jabotinsky equations, iteration sequences, groups and semigroups of iterates, cellular automata, connections with functional analysis, phantom iterates. An appendix briefly discusses various topics which are outside the main fields like: numerical methods, dynamics in one or two dimensions, complex iteration, fractal sets, and experimental mathematics.
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39-02
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 68Q80
zbMATH DE Number: 794223
zbMATH Keywords: iteration theory
zbMATH Keywords: orbit theory
zbMATH Keywords: algebraic iteration theory
zbMATH Keywords: iteration of formal power series
zbMATH Keywords: Pilgerschritt transformation
zbMATH Keywords: Aczél-Jabotinsky equations
zbMATH Keywords: iteration sequences
zbMATH Keywords: groups and semigroups of iterates
zbMATH Keywords: cellular automata
zbMATH Keywords: phantom iterates
zbMATH Keywords: numerical methods
zbMATH Keywords: complex iteration
zbMATH Keywords: fractal sets
zbMATH Keywords: experimental mathematics
reviewed by: Marek Cezary Zdun
MaRDI profile type: Publication
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Progress of iteration theory since 1981 (OpenAlex ID)
OpenAlex ID: W4211071348