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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.|
|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|
|Pages:||1343 - 1374|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY|
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