%0 Journal Article
%T Discrepancy estimate of normal vectors
%A Mordechay B. Levin
%A Irina L. Volinsky
%J Uniform Distribution Theory
%D 2008
%I Mathematical Institute of the Slovak Academy of Sciences
%X Let $A$ be an $s \times s$ invertible matrix with integer entries and with eigenvalues $|\lambda_i| > 1, i=1, \ldots,s$. In this paper we prove explicitly that there exists a vector $\alpha$, such that the discrepancy of the sequence $\{\alpha A^n\}_{n=1}^{N}$ is equal to $O(N^{-1} (\log N)^{2s+3})$ for $N \longrightarrow \infty$. This estimate can be improved no more than on the logarithmic factor.
%K Ergodic matrix
%K normal vector
%K discrepancy
%U http://www.boku.ac.at/MATH/udt/vol03/no1/LevVol08-1.pdf