no. 1

Substitution invariant cutting sequences
Journal de Théorie des Nombres de Bordeaux, Tome 5 (1993) no. 1, pp. 123-137. 
@article{JTNB_1993__5_1_123_0,
     author = {Crisp, D. and Moran, W. and Pollington, A. D. and Shiue, P.},
     title = {Substitution invariant cutting sequences},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {123--137},
     publisher = {Universit\'e Bordeaux I},
     volume = {5},
     number = {1},
     year = {1993},
     zbl = {0786.11041},
     mrnumber = {1251232},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_1993__5_1_123_0/}
}
Crisp, D.; Moran, W.; Pollington, A.; Shiue, P. Substitution invariant cutting sequences. Journal de Théorie des Nombres de Bordeaux, Tome 5 (1993) no. 1, pp. 123-137. http://archive.numdam.org/item/JTNB_1993__5_1_123_0/

[1] T.C. Brown, A characterisation of the quadratic irrationals, Canad. Math. Bull. 34 (1991), 36-41. | MR 1108926 | Zbl 0688.10007

[2] H. Cohn, Some direct limits of primitive homotopy words and of Markoff geodesics, Discontinuous groups and Riemann surfaces, Ann. of Math. Studies No. 79, Princeton Univ. Press, Princeton, N.J., (1974), 81-98. | MR 369269 | Zbl 0294.20044

[3] A.S. Fraenkel, Determination of [nθ] by its sequence of differences, Canad. Math. Bull. 21 (1978), 441-446. | Zbl 0401.10018

[4] Sh. Ito and S. Yasutomi, On continued fractions, substitutions and characteristic sequences [nx + y] - [(n - 1)x + y], Japan J. Math. 16 (1990), 287-306. | MR 1091163 | Zbl 0721.11009

[5] C. Series, The geometry of Markoff numbers, Math. Intelligencer 7 (1985), 20-29. | MR 795536 | Zbl 0566.10024

[6] K.B. Stolarsky, Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull. 19 (1976), 473-482. | MR 444558 | Zbl 0359.10028