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Rauzy’s conjecture on billiards in the cube. (English) Zbl 0814.11014
The authors prove a theorem conjectured by G. Rauzy [see Sémin. Théor. Nombres, Univ. Bordeaux I 1982-1983, Exp. No. 25 (1983; Zbl 0547.10048); Lect. Notes Comput. Sci. 192, 165-171 (1985; Zbl 0613.10044)], which describes the complexity of sequences defined by billiards in the cube. The initial proof of Rauzy’s conjecture was given by the same authors using ergodic arguments on a dynamical system.

MSC:
11B85 Automata sequences
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