Geodesic
On the first return times for toric rotations
Čebyševskij sbornik, Tome 14 (2013) no. 4, pp. 127-130.

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Some examples of domains such that first return time function for two-dimensional torus shift has at most three values are constructed. Some applications to bounded remainder sets problem are obtained.
Keywords: bounded remainder sets, first return time. 
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D. V. Kuznetsova; A. V. Shutov. On the first return times for toric rotations. Čebyševskij sbornik, Tome 14 (2013) no. 4, pp. 127-130. http://geodesic.mathdoc.fr/item/CHEB_2013_14_4_a8/

[1] Floreik K., “Une remarque sur la repartition des nombres $m\xi \mod 1$”, Coll. Math. Wroclaw, 2 (1951), 323–324

[2] Shutov A. V., “Derivatives of Circle Rotations and the Similarity of Orbits”, Journal of Mathematical Sciences, 133, March (2006), 1765–1771 | DOI | MR