Ergodic Properties of Square-Free Numbers
Dynamical Systems
2013-04-08 v2 Number Theory
Abstract
We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This implies that this system is not weakly mixing and has zero measure-theoretical entropy.
Keywords
Cite
@article{arxiv.1112.4691,
title = {Ergodic Properties of Square-Free Numbers},
author = {Francesco Cellarosi and Yakov G. Sinai},
journal= {arXiv preprint arXiv:1112.4691},
year = {2013}
}
Comments
37 page, 1 figure