Some dynamical properties of Benford sequences
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Bibliographic record
Abstract
Abstract Numerical data generated by dynamical processes often obey Benford's law of logarithmic mantissa distributions. For non-autonomous difference equations this article presents necessary as well as sufficient conditions for to conform with Benford's law in its strongest form: The proportion of values in with base b mantissa less than t tends to as , for all integer bases . The assumptions on , 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. Keywords: Benford's lawBenford sequenceuniform distribution mod 1non-autonomous dynamical systemshadowingAMS Subject Classification:: 11K0637A4537B55
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