One-Dimensional Dynamical Systems and Benford's Law

  title={One-Dimensional Dynamical Systems and Benford's Law},
  author={Arno Berger and Leonid A. Bunimovich and Theodore P. Hill},
One-dimensional projections of (at least) almost all orbits of many multi- dimensional dynamical systems are shown to follow Benford's law, i.e. their (base b) mantissa distribution is asymptotically logarithmic, typically for all bases b. As a generalization and uniflcation of known results it is proved that under a (generic) non-resonance condition on A 2C d£d , for every z 2C d real and imaginary part of each non-trivial component of (A n z)n2N0 and (e At z)t‚0 follow Benford's law. Also… CONTINUE READING


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Publications referenced by this paper.

On Mantissa Distributions in Computing and Benford's Law

  • Elektronische Informationsverarbeitung und Kybernetik
  • 1988

The distribution of leading digits and uniform distribution mod 1

R. Tichy
  • Ann . Probab .
  • 1979

The law of anomalous numbers

A. Berger
  • Proceedings of the American Philosophical Society
  • 1938

Note on the frequency of use of the different digits in natural numbers

R. Raimi
  • Amer . J . Math .