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 | References | Similar Articles | Additional Information
Abstract: We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with elements. For a permutation, this entropy turns out to be asymptotically (for a growing number of iterations) close to
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