Iteration entropy

Published 4 Dec 2017 in math.NT | (1712.01407v2)

Abstract: We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to \log_2(n) minus the entropy of the vector of its cycle lengths. For general functions, a similar approximation holds.

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Joachim von zur Gathen

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