Benford's law in power-like dynamical systems

  • Berger A
Citations of this article
Mendeley users who have this article in their library.
Get full text


A generalized shadowing lemma is used to study the generation of Benford<br />sequences under non-autonomous iteration of power-like maps T-j : x -><br />alpha(j)x(beta j) (1 - f(j) (x)), with alpha(j), beta(j) > 0 and f(j) is<br />an element of C-1, f(j) (0) = 0, near the fixed point at x = 0. Under<br />mild regularity conditions almost all orbits close to the fixed point<br />asymptotically exhibit Benford's logarithmic mantissa distribution with<br />respect to all bases, provided that the family (T-j) is contracting on<br />average, i.e. lim(n)->infinity n(-1) Sigma(j)(-1)(n)=1 log beta(j) > 0.<br />The technique presented here also applies if the maps are chosen at<br />random, in which case the contraction condition reads Elogo > 0. These<br />results complement, unify and widely extend previous work. Also, they<br />supplement recent empirical observations in experiments with and<br />simulations of deterministic as well as stochastic dynamical systems.




Berger, A. (2005). Benford’s law in power-like dynamical systems. STOCHASTICS AND DYNAMICS, 5(4), 587–607.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free