Ergodic Properties of Square-Free Numbers

Details Ergodic Properties of Square-Free Numbers Ergodic Properties of Square-Free Numbers

2011-12-20

arxiv.org/abs/1112.4691v1

Mathematics

Dynamical Systems

37 page, 1 figure

Scientific paper

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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