One-dimensional Dynamical Systems and Benford ’ S Law

@inproceedings{Bunimovich2005OnedimensionalDS,
  title={One-dimensional Dynamical Systems and Benford ’ S Law},
  author={L. A. Bunimovich and Theodore P. Hill},
  year={2005}
}
Near a stable fixed point at 0 or ∞, many real-valued dynamical systems follow Benford's law: under iteration of a map T the proportion of values in {x, T (x), T 2 (x),. .. , T n (x)} with mantissa (base b) less than t tends to log b t for all t in [1, b) as n → ∞, for all integer bases b > 1. In particular , the orbits under most power, exponential, and rational functions (or any successive combination thereof), follow Benford's law for almost all sufficiently large initial values. For… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 12 references

The distribution of leading digits and uniform distribution mod 1

  • P. Diaconis
  • Ann . Probab .
  • 1979

Probability Theory II . Springer , New York

  • M. Loéve
  • 1978

The first digit problem

  • R. Raimi
  • Amer . Math . Monthly
  • 1976

Modulo one uniform distribution of the sequence of logarithms of certain recursive sequences

  • J. Brown, R. Duncan
  • Fibonacci Quarterly
  • 1970

The law of anomalous numbers

  • F. Benford
  • Proceedings of the American Philo ­ sophical…
  • 1938

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