Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2007-10

April 2007

How many times can a function be iterated?

Massimo Gobbino and Robert Samuel Simon

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.

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