Geodesic
Ergodic properties of square-free numbers
Journal of the European Mathematical Society, Tome 15 (2013) no. 4, pp. 1343-1374.

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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.
DOI : 10.4171/jems/394
Classification : 37-XX, 28-XX, 00-XX
Keywords: Square-free numbers, correlation functions, dynamical systems with pure point spectrum, ergodicity 
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     author = {Francesco Cellarosi and Yakov G. Sinai},
     title = {Ergodic properties of square-free numbers},
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Francesco Cellarosi; Yakov G. Sinai. Ergodic properties of square-free numbers. Journal of the European Mathematical Society, Tome 15 (2013) no. 4, pp. 1343-1374. doi : 10.4171/jems/394. http://geodesic.mathdoc.fr/articles/10.4171/jems/394/

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