How many times can a function be iterated?

Details How many times can a function be iterated? How many times can a function be iterated?

2009-01-21

arxiv.org/abs/0901.3230v3

Mathematics

Dynamical Systems

28 pages, 8 figures, section with applications to game theory rewritten, references updated. To appear on the Journal of Diffe

Scientific paper

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) lies in C for every x in the boundary of 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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