Ergodic properties of square-free numbers | Zendy

Francesco Cellarosi | Zendy; Yakov G. Sinai | Zendy

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Ergodic properties of square-free numbers

Author(s) -

Francesco Cellarosi,

Yakov G. Sinai

Publication year - 2013

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/394

Subject(s) - mathematics , ergodic theory , invariant measure , abelian group , square free integer , invariant (physics) , pure mathematics , entropy (arrow of time) , square (algebra) , discrete mathematics , mathematical analysis , geometry , mathematical physics , physics , quantum mechanics

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.

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