Discrete and Continuous Dynamical Systems 13(1), 219-237
ISSN / ISBN: 1078-0947
ABSTRACT: 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 unification of known results it is proved that under a (generic) non-resonance condition on A ∈ Cd × d, for every z ∈ Cd real and imaginary part of each non-trivial component of (Anz)n ∈ N and (eAtz)t ≥ 0 follow Benford's law. Also, Benford behavior is found to be ubiquitous for several classes of non-linear maps and differential equations. In particular, emergence of the logarithmic mantissa distribution turns out to be generic for complex analytic maps T with T(0)=0, |T'(0)|<1. The results significantly extend known facts obtained by other, e.g. number-theoretical methods, and also generalize recent findings for one-dimensional systems
Bibtex not available at this time.
Reference Type: Journal Article
Subject Area(s): Analysis, Dynamical Systems