Progress of iteration theory since 1981
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.
scientific article; zbMATH DE number 794223
scientific article