Développement en base θ, répartition modulo un de la suite (xθ n ), n≥0, langages codés et θ-shift
Bertrand-Mathis, Anne
Bulletin de la Société Mathématique de France, Tome 114 (1986), p. 271-323 / Harvested from Numdam
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@article{BSMF_1986__114__271_0,
     author = {Bertrand-Mathis, Anne},
     title = {D\'eveloppement en base $\theta $, r\'epartition modulo un de la suite $(x\theta ^n)$, n$\ge 0$, langages cod\'es et $\theta $-shift},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {114},
     year = {1986},
     pages = {271-323},
     doi = {10.24033/bsmf.2058},
     mrnumber = {88e:11067},
     zbl = {0628.58024},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/BSMF_1986__114__271_0}
}

Bertrand-Mathis, Anne. Développement en base $\theta $, répartition modulo un de la suite $(x\theta ^n)$, n$\ge 0$, langages codés et $\theta $-shift. Bulletin de la Société Mathématique de France, Tome 114 (1986) pp. 271-323. doi : 10.24033/bsmf.2058. http://gdmltest.u-ga.fr/item/BSMF_1986__114__271_0/

[1] A. Rényi. Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar, vol. 8, 1957, p. 401-414. | MR 20 #3843 | Zbl 0079.08901

[2] W. Parry. On the β-expansion of real numbers, Acta Math. Acad. Sci. Hungar., vol. 11, 1960, p. 401-416. | MR 26 #288 | Zbl 0099.28103

[3] Ito Takahashi, Markov subshifts and realization of β-expansions, J. Math. Soc. Japan, vol. 26, n 1, 1974. | Zbl 0269.28006

[4] Hofbauer, Maximal mesures for simple piecewise monotonic transformations, Z. Wahrschein. Verw Gebiete, vol. 52, 1980, n 3. | MR 81f:28023 | Zbl 0415.28018

[5] F. Blanchard, G. Hansel, Systèmes codés (à paraître).

[6] S. Eilenberg, Automata, langages and machines, vol. A, London Academic Press, 1974. | Zbl 0317.94045

[7] Sigmund, On the Distribution of periodic points for β-shifts, Monatshefte für Mathematik, vol. 82, 1976, p. 247-252. | MR 54 #5442 | Zbl 0333.58008

[8] J. M. Franks, Homology an dynamical systems, conference board of the mathematical sciences published by the American Mathematical Society.

[9] J.-P. Kahane, R. Salem, Ensembles parfaits et séries trigonométriques, Paris, Hermann, 1963. | Zbl 0112.29304

[10] K. Schmidt, On periodic expansions of Pisot numbers and Salem numbers. | Zbl 0494.10040

[11] J. W. S. Cassels, An introduction to diophantine approximation, Cambridge Univ. Press, London, 1957. | Zbl 0077.04801

[12] D. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc., vol. 8, 1950, p. 254-260. | Zbl 0007.33701

[13] M. Mendes France, T. Kamae, Van Der Corput, Difference Theorem, Israel J. of Math., 1978-1979, p. 31-32. | Zbl 0396.10040

[14] A. Bertrand-Mathis, Mesure de Champernowne sur certains systèmes codés (à paraître).

[15] M. Mendes France, Thèse, Israel J. of Math., 1966.

[16] S. Ito, I. Shiokawa, A construction of β-normal sequence, J. Math. Soc. Japan, vol. 27, no 1, 1975. | Zbl 0292.10040

[17] Y. Meyer, Nombres algébriques et Analyse harmonique, Ann. Scient. Ec. Norm. Sup., 4e année, t. 3, 1970, p. 75-110. | Numdam | Zbl 0197.32702

[18] Y. Takahashi, Shift with orbit basis and realization of one dimensional maps, Osaka J. Math., 20, 1983, p. 599-629 | Zbl 0547.58031