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MR2291158 (2008f:37080) 37D50 (37B10 37E99)
Gutkin, Eugene; Tabachnikov, Serge Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards on surfaces of constant curvature. Mosc. Math. J. 6 (2006), no. 4, 673–701, 772.
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