Journal of Difference Equations and Applications 17(2), pp. 137-159.
ISSN/ISBN: Not available at this time. DOI: 10.1080/10236198.2010.549012
Abstract: Numerical data generated by dynamical processes often obey Benford’s law of logarithmic mantissa distributions. For non-autonomous difference equations x_{n}=T(x_{n-1}), n=1,2,..., this article presents necessary as well as sufficient conditions for (x_{n}) to conform with Benford’s law in its strongest form: The proportion of values in {x_{0}, x_{1}, ... , x_{n}} with base b mantissa less than t tends to logb t as n⟶∞, for all integer bases b>1. The assumptions on (T_{n}), viz. asymptotic convexity and eventual expansivity on average, are very mild and met, e.g. by practically all polynomial, rational and exponential maps and any combinations thereof. The results complement, extend and unify previous work.
Bibtex:
@article {MR2783341,
AUTHOR = {Berger, Arno},
TITLE = {Some dynamical properties of {B}enford sequences},
JOURNAL = {J. Difference Equ. Appl.},
FJOURNAL = {Journal of Difference Equations and Applications},
VOLUME = {17},
YEAR = {2011},
NUMBER = {2},
PAGES = {137--159},
ISSN = {1023-6198},
MRCLASS = {37A45 (11K06)},
MRNUMBER = {2783341 (2012h:37014)},
DOI = {10.1080/10236198.2010.549012},
URL = {http://dx.doi.org/10.1080/10236198.2010.549012},
}
Reference Type: Journal Article
Subject Area(s): Dynamical Systems