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
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
Copyright © 2006 Stefano Isola. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.