One-dimensional Dynamical Systems and Benford ’ S Law

  title={One-dimensional Dynamical Systems and Benford ’ S Law},
  author={L. A. Bunimovich and Theodore P. Hill},
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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