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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Iteration entropy


Author: Joachim von zur Gathen
Journal: Math. Comp. 88 (2019), 1991-2003
MSC (2010): Primary 11K45, 37P25, 68W20, 94A60
DOI: https://doi.org/10.1090/mcom/3382
Published electronically: October 30, 2018
MathSciNet review: 3925494
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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, this entropy turns out to be 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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Additional Information

Joachim von zur Gathen
Affiliation: B-IT, Universität Bonn, Endenicher Allee 19c, 53115 Bonn, Germany
Email: gathen@bit.uni-bonn.de

DOI: https://doi.org/10.1090/mcom/3382
Received by editor(s): December 31, 2017
Received by editor(s) in revised form: May 10, 2018
Published electronically: October 30, 2018
Article copyright: © Copyright 2018 American Mathematical Society