Ergodic Properties of Square-Free Numbers

Autor:	Cellarosi, Francesco, Sinai, Yakov G.
Rok vydání:	2011
Předmět:	Mathematics - Dynamical Systems Mathematics - Number Theory 37A35 37A45 28D99
Druh dokumentu:	Working Paper
Popis:	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. Comment: 37 page, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1112.4691 Zobrazit plný text záznamu View this record from Arxiv