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International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 20568, 20 pages
doi:10.1155/IJMMS/2006/20568

Dispersion properties of ergodic translations

Stefano Isola

Dipartimento di Matematica e Informatica, Università di Camerino, via Madonna delle Carceri, Camerino 62032, Italy

Received 19 November 2005; Revised 23 January 2006; Accepted 25 January 2006

Abstract

We consider irrational rotations of the circle Tx=x+α (mod⁡ 1) and study the asymptotic behavior of sums of the type Sn=∑k=0n−1πk with πk=±1, the sign being determined by the location of Tkx with respect to a binary partition.