Ergodic properties of square-free numbers

Cellarosi, Francesco, and Sinaj, Jakov G.. "Ergodic properties of square-free numbers." Journal of the European Mathematical Society 015.4 (2013): 1343-1374. <http://eudml.org/doc/277274>.

@article{Cellarosi2013,
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.},
author = {Cellarosi, Francesco, Sinaj, Jakov G.},
journal = {Journal of the European Mathematical Society},
keywords = {square-free numbers; correlation functions; dynamical systems with pure point spectrum; ergodicity; square-free numbers; correlation functions; dynamical systems with pure point spectrum; ergodicity},
language = {eng},
number = {4},
pages = {1343-1374},
publisher = {European Mathematical Society Publishing House},
title = {Ergodic properties of square-free numbers},
url = {http://eudml.org/doc/277274},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Cellarosi, Francesco
AU - Sinaj, Jakov G.
TI - Ergodic properties of square-free numbers
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 4
SP - 1343
EP - 1374
AB - 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.
LA - eng
KW - square-free numbers; correlation functions; dynamical systems with pure point spectrum; ergodicity; square-free numbers; correlation functions; dynamical systems with pure point spectrum; ergodicity
UR - http://eudml.org/doc/277274
ER -