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Ergodic properties of square-free numbers

Author(s): Cellarosi, F; Sinai, Yakov G

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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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