English

Most linear flows on $\mathbb{R}^d$ are Benford

Dynamical Systems 2015-01-23 v1 Classical Analysis and ODEs

Abstract

A necessary and sufficient condition ("exponential nonresonance") is established for every signal obtained from a linear flow on Rd\mathbb{R}^d by means of a linear observable to either vanish identically or else exhibit a strong form of Benford's Law (logarithmic distribution of significant digits). The result extends and unifies all previously known (sufficient) conditions. Exponential nonresonance is shown to be typical for linear flows, both from a topological and a measure-theoretical point of view.

Keywords

Cite

@article{arxiv.1501.05345,
  title  = {Most linear flows on $\mathbb{R}^d$ are Benford},
  author = {Arno Berger},
  journal= {arXiv preprint arXiv:1501.05345},
  year   = {2015}
}

Comments

26 pages

R2 v1 2026-06-22T08:09:09.594Z