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Berger, A (2005)

Benford’s Law in power-like dynamical systems

Stochastics and Dynamics 5, pp. 587-607.

ISSN/ISBN: 0219-4937 DOI: 10.1142/S0219493705001602

Abstract: A generalized shadowing lemma is used to study the generation of Benford sequences under non-autonomous iteration of power-like maps Tj: x → αj xβj(1- fj(x)), with αj, βj > 0 and fj ∈ C1, fj (0) = 0, near the fixed point at x = 0. Under mild regularity conditions almost all orbits close to the fixed point asymptotically exhibit Benford’s logarithmic mantissa distribution with respect to all bases, provided that the family (Tj) is contracting on average, i.e. limn → ∞ n-1j=1n log j > 0.The technique presented here also applies if the maps are chosen at random, in which case the contraction condition reads E log β > 0. These results complement, unify and widely extend previous work. Also, they supplement recent empirical observations in experiments with and simulations of deterministic as well as stochastic dynamical systems.

@article {MR2185507, AUTHOR = {Berger, Arno}, TITLE = {Benford's law in power-like dynamical systems}, JOURNAL = {Stoch. Dyn.}, FJOURNAL = {Stochastics and Dynamics}, VOLUME = {5}, YEAR = {2005}, NUMBER = {4}, PAGES = {587--607}, ISSN = {0219-4937}, MRCLASS = {37B55 (11K06 37A50 37E05)}, MRNUMBER = {2185507 (2008i:37029)}, MRREVIEWER = {Peter Raith}, DOI = {10.1142/S0219493705001602}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Analysis, Dynamical Systems