Centre for Discrete and Applicable Mathematics 

CDAM Research Report, LSECDAM200710April 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 setvalued maps.
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