no. 2
An improved estimate on the distribution mod 1 of powers of real matrices
Compositio Mathematica, Tome 49 (1983) no. 2, pp. 283-289. 
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     author = {Nowak, Werner Georg and Tichy, Robert Franz},
     title = {An improved estimate on the distribution mod 1 of powers of real matrices},
     journal = {Compositio Mathematica},
     pages = {283--289},
     publisher = {Martinus Nijhoff Publishers},
     volume = {49},
     number = {2},
     year = {1983},
     mrnumber = {704394},
     zbl = {0496.10034},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1983__49_2_283_0/}
}
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Nowak, Werner Georg; Tichy, Robert Franz. An improved estimate on the distribution mod 1 of powers of real matrices. Compositio Mathematica, Tome 49 (1983) no. 2, pp. 283-289. http://archive.numdam.org/item/CM_1983__49_2_283_0/

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[2] E. Hlawka: Theorie der Gleichverteilung. Mannheim- Wien-Zürich, Bibl. Inst. 1979. | MR | Zbl

[3] L. Kuipers and H. Niederreiter: Uniform distribution of sequences. New York-Sydney-Toronto, John Wiley and Sons 1974. | MR | Zbl

[4] W.J. Le Veque: The distribution mod 1 of trigonometric sequences. Duke Math. Journal 20 (1953) 367-374. | Zbl

[5] V. Losert, W.G. Nowak and R.F. Tichy: On the asymtotic distribution of the powers of (s x s)-matrices. Comp. Math., to appear. | Numdam | Zbl