Geodesic
On distribution of fractional parts of linear forms
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 123-137.

Voir la notice de l'article provenant de la source Math-Net.Ru

The Peres–Schlag's approach is used to construct badly approximable numbers in various problems of Diophantine approximation. 
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I. P. Rochev. On distribution of fractional parts of linear forms. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 123-137. http://geodesic.mathdoc.fr/item/FPM_2010_16_6_a9/

[1] Kassels Dzh. V. S., Vvedenie v teoriyu diofantovykh priblizhenii, IL, M., 1961

[2] Moschevitin N. G., “O raspredelenii po modulyu 1 lakunarnykh i sublakunarnykh posledovatelnostei: primenenie konstruktsii Peresa–Shlaga”, Fundament. i prikl. mat., 16:5 (2010), 117–138

[3] Khinchin A. Ya., Izbrannye trudy po teorii chisel, MTsNMO, M., 2006 | MR

[4] Peres Y., Schlag W., Two Erdős problems on lacunary sequences: Chromatic number and Diophantine approximation, Preprint, 2007, arXiv: 0706.0223v1[math.CO]