Sur les transformations linéaires modulo un
Annales de l'I.H.P. Probabilités et statistiques, Volume 15 (1979) no. 2, p. 187-193
@article{AIHPB_1979__15_2_187_0,
     author = {Cabane, R.},
     title = {Sur les transformations lin\'eaires modulo un},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {15},
     number = {2},
     year = {1979},
     pages = {187-193},
     zbl = {0414.28020},
     mrnumber = {548471},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPB_1979__15_2_187_0}
}
Cabane, R. Sur les transformations linéaires modulo un. Annales de l'I.H.P. Probabilités et statistiques, Volume 15 (1979) no. 2, pp. 187-193. http://www.numdam.org/item/AIHPB_1979__15_2_187_0/

[1] A. Renyl, Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar, t. 8, 1957, p. 477-493. | MR 97374 | Zbl 0079.08901

[2] W. Parry, Representations for real numbers. Acta. Math. Acad. Sci. Hungar., t. 15, 1964, p. 95-105. | MR 166332 | Zbl 0136.35104

[3] M. Smorodinsky, β-automorphisms are Bernoulli. Acta. Math. Acad. Sci. Hungar., t. 24, 1973, p. 273-278. | MR 346133 | Zbl 0268.28007

[4] K.M. Wilkinson, Ergodic properties of certain linear modulo one transformations. Adv. in Math., t. 14, 1974, p. 64-72. | MR 344421 | Zbl 0286.28009

[5] M. Ratner, Bernoulli flows over maps of the interval. Israel Journal of Math., t. 31, 1978, p. 298-313. | MR 516152 | Zbl 0435.58022

[6] A. Lasota, Y. Yorke, On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc., t. 186, 1973, p. 481-488. | MR 335758 | Zbl 0298.28015

[7] Z.S. Kowalski, Invariant measures for piecewise monotonic transformations, 1975, Springer Lecture Notes 472, 77-94. | MR 390173 | Zbl 0309.28004

[8] Z.S. Kowalski, Some remarks about the invariant measures for piecewise monotonic transformations. Bull. Acad. Pol. Sci. Ser. Math., t. 25, n° 1, 1977, p. 7-12. | MR 430212 | Zbl 0349.28012

[9] R. Bowen, Bernoulli maps of the unit interval. Israel Journal of Math., t. 28, 1977, p. 161-168. | MR 453974 | Zbl 0377.28010