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How many times can a function be iterated?

By Robert Simon

Abstract

Let C be a closed subset of a topological space X, and let f : C → X. Let us assume that f is continuous and f(x) ∈ C for every x ∈ ∂C. How many times can one iterate f? This paper provides estimates on the number of iterations and examples of their optimality. In particular we show how some topological properties of f, C, X are related to the maximal number of iterations, both in the case of functions and in the more general case of set-valued maps

Topics: H Social Sciences (General)
Publisher: London School of Economics and Political Science
Year: 2007
OAI identifier: oai:eprints.lse.ac.uk:6900
Provided by: LSE Research Online
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