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http://arks.princeton.edu/ark:/88435/pr1709v| 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. |
| Publication Date: | 2013 |
| Electronic Publication Date: | 9-May-2013 |
| Citation: | Cellarosi, F, Sinai, Ya G. (2013). Ergodic properties of square-free numbers. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 15 (1343 - 1374. doi:10.4171/JEMS/394 |
| DOI: | doi:10.4171/JEMS/394 |
| ISSN: | 1435-9855 |
| Pages: | 1343 - 1374 |
| Type of Material: | Journal Article |
| Journal/Proceeding Title: | JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY |
| Version: | Author's manuscript |
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