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Hi Famous iterated functions include the Mandelbrot set and Iterated function systems. If f is the action of a group element on a set, then the iterated function corresponds to a free group. Iterated functions can be studied with the Artin-Mazur zeta function and with transfer operators. In computer science, iterated functions occur as a special case of recursive functions, which in turn anchor the study of such broad topics as lambda calculus, or narrower onces, such as the denotational semantics of computer programs.
=Ron
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