Dynamics and digits: On the surprising ubiquity of Benford's Law
by
Arno Berger
Institute of Mechanics, Vienna University of Technology

Significant digits and mantissae in sufficiently large and diverse aggregations of numerical data are not equally likely, as might be expected, but rather follow a logarithmic distribution surprisingly often. This empirical observation, commonly referred to as Benford's Law, is addressed in the context of dynamical systems (both in continuous and discrete time). A tailor-made shadowing technique and standard tools of uniform distribution theory are utilized to show that Benford's logarithmic mantissa distribution is in fact ubiquitous for regular systems; it should however not be expected to emerge for classical chaotic systems.

Date received: June 12, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calt-03.