Suites algébriques, automates et substitutions
Bulletin de la Société Mathématique de France, Tome 108 (1980), p. 401-419
@article{BSMF_1980__108__401_0,
     author = {Christol, Gilles and Kamae, Teturo and Mend\`es France, Michel and Rauzy, G\'erard},
     title = {Suites alg\'ebriques, automates et substitutions},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {108},
     year = {1980},
     pages = {401-419},
     doi = {10.24033/bsmf.1926},
     zbl = {0472.10035},
     mrnumber = {82e:10092},
     language = {fr},
     url = {http://http://www.numdam.org/item/BSMF_1980__108__401_0}
}
Christol, G.; Kamae, T.; Mendès France, Michel; Rauzy, Gérard. Suites algébriques, automates et substitutions. Bulletin de la Société Mathématique de France, Tome 108 (1980) pp. 401-419. doi : 10.24033/bsmf.1926. http://www.numdam.org/item/BSMF_1980__108__401_0/

[1] Baum (L.) et Sweet (M.). - Continued fractions of algebraic power series in characteristic 2, Ann. Math., t. 103, 1976, p. 593-610. | MR 53 #13127 | Zbl 0312.10024

[2] Baum (L.), Herzberg (N.), Lomonaco Jr (S.) et Sweet (M.). - Fields of almost periodic sequences, J. Combinat. Theory (A), t. 22, 1977, p. 169-180. | MR 58 #258 | Zbl 0354.12020

[3] Brillhart (J.) et Carlitz (L.). - Note on the Shapiro polynomials. Proc. Am. Math. Soc., t. 25, 1970, p. 114-118. | MR 41 #5575 | Zbl 0191.35101

[4] Christol (G.). - Ensembles presque périodiques k-reconnaissables, Theoretical Computer Science, t. 9, 1979, p. 141-145. | MR 80e:68141 | Zbl 0402.68044

[5] Cobham (A.). - On the base-dependence of sets of numbers recognizable by finite automata, Mathem. Syst. Theory, t. 3, 1969, p. 186-192. | MR 40 #4021 | Zbl 0179.02501

[6] Cobham (A.). - Uniform tag sequences, Mathem. Syst. Theory, t. 6, 1972, p. 164-192. | MR 56 #15230 | Zbl 0253.02029

[7] Conway (J. H.). - Regular algebra and Finite machines, Chapman and Hall, 1971. | Zbl 0231.94041

[8] Coquet (J.), Kamae (T.) et Mendes France (M.). - Sur la mesure spectrale de certaines suites arithmétiques, Bull. Soc. Math. France, t. 105, 1977, p. 369-384. | Numdam | MR 57 #12439 | Zbl 0383.10035

[9] Dekking (M.). - Transcendance du nombre de Thue-Morse, C. R. Acad. Sc., Paris, t. 285, 1977, série A, p. 157-160. | MR 56 #15571 | Zbl 0362.10028

[10] Eilenberg (S.). - Automata, Languages and Machines, vol. A, 1974, Academic Press. | MR 58 #26604a | Zbl 0317.94045

[11] Fliess (M.). - Sur divers produits de séries formelles, Bull. Soc. Math. France, t. 102, 1974, p. 181-191. | Numdam | MR 50 #7125 | Zbl 0313.13021

[12] Furstenberg (H.). - Algebraic functions over finite fields, J. Algebra, t. 7, 1967, p. 271-277. | MR 35 #6655 | Zbl 0175.03903

[13] Gottschalk (W. H.) et Hedlung (G. A.). - Topological dynamics, Amer. Math. Soc. Colloquium Publications, t. 36, 1955. | MR 17,650e | Zbl 0067.15204

[14] Hedlund (G. A.). - Remarks on the work of Axel Thue on sequences, Nordisk Mat. Tidskr., t. 15, 1967, p. 148-150. | MR 37 #4454 | Zbl 0153.33101

[15] Kakutani (S.). - Ergodic theory of shift transformations, Proceedings of the 5th Berkeley symposium on mathematical statistics and probability [1965, Berkeley], p. 405-414, Berkeley, University of California Press. | MR 37 #2943 | Zbl 0217.38004

[16] Kakutani (S.). - Strictly ergodic symbolic dynamical systems, Proceedings of the 6th Berkeley symposium on mathematical statistics and probability [1970, Berkeley], vol. 2, p. 319-326, Berkeley, University of California Press. | MR 53 #8383 | Zbl 0262.28014

[17] Kamae (T.). - Spectrum of a substitution minimal set, J. Math. Soc. Japan, t. 22, 1970, p. 567-578. | MR 44 #3308 | Zbl 0197.49901

[18] Kamae (T.). - A topological invariant of substitution minimal sets, J. Math. Soc. Japan, t. 24, 1972, p. 285-306. | MR 45 #2688 | Zbl 0232.54052

[19] Kamae (T.). - Subsequences of normal sequences, Israel J. of Math., t. 16, 1973, p. 121-149. | MR 49 #3086 | Zbl 0272.28012

[20] Keane (M.). - Generalized Morse sequences, Z. Wahrscheinlichkeitstheorie, t. 10, 1968, p. 335-353. | MR 39 #406 | Zbl 0162.07201

[21] Kubota (K. K.). - An application of Kronecker's theorem to transcendence theory, Séminaire Théorie des Nombres, Bordeaux, 1975-1976, exposé 25. | Zbl 0356.10030

[22] Lang (S.). - Algebraic numbers, 1964, Addison-Werley. | MR 28 #3974 | Zbl 0211.38501

[23] Mahler (K.). - On the translation properties of a simple class of arithmetical functions, J. Math. and Phys., t. 6, 1927, p. 158-163. | JFM 53.0265.03

[24] Martin (J.). - Generalized Morse sequences on n symbols, Proc. Am. Math. Soc., t. 54, 1976, p. 379-383. | MR 52 #11880 | Zbl 0317.54054

[25] Martin (J.). - The structure of generalized Morse minimal sets on n symbols, Trans. Am. Math. Soc., t. 232, 1977, p. 343-355. | MR 57 #3352 | Zbl 0375.28010

[26] Morse (M.). - Recurrent geodesics on a surface of negative curvature, Trans. Am. Math. Soc., t. 22, 1921, p. 84-100. | JFM 48.0786.06 | MR 1501161

[27] Queffelec (M.). - Mesures spectrales associées à certaines suites arithmétiques, Bull. Soc. Math. France, t. 107, 1979, p. 385-421. | Numdam | MR 81c:10071 | Zbl 0435.42007

[28] Rauzy (G.). - Nombres normaux et processus déterministes, Acta Arith., t. 29, 1976, p. 211-225. | MR 53 #7995 | Zbl 0287.10049

[29] Rauzy (G.). - Propriétés statistiques de suites arithmétiques, Collection SUP, Le Mathématicien, t. 15, 1976, Presses Univ. de France. | MR 53 #13152 | Zbl 0337.10036

[30] Rauzy (G.). - Une généralisation du développement en fraction continue, Séminaire Théorie des Nombres, Delange-Pisot-Poitou, 1976, Paris. | Numdam | Zbl 0369.28015

[31] Rudin (W.). - Some theorems on Fourier coefficients, Proc. Am. Math. Soc., t. 10, 1959, p. 855-859. | MR 22 #6979 | Zbl 0091.05706

[32] Shapiro (H. S.). - Extremal problems for polynomials and power series, Thesis MIT, 1951.

[33] Thue (A.). - Über die gegenseitige lage gleicher Teile gewisser Zeichenreichen Videnskabsselskabets Skrifter I Mat. nat. Kl., Christiania, 1906.

[34] Van Der Poorten (A.). - Propriétés arithmétiques et algébriques de fonctions satisfaisant une classe d'équations fonctionnelles, Séminaire Théorie des Nombres, Bordeaux, 1974-1975, exposé 7. | Zbl 0331.10018

[35] Wiener (N.). - Generalized Harmonic Analysis, Acta Mathem., t. 55, 1930, p. 117-258 (en particulier p. 204-209). | JFM 56.0954.02