Nous donnons une caractérisation complète de tous les morphismes binaires qui préservent les mots sturmiens et montrons que les mots infinis engendrés par ces morphismes sont rigides.
We give a complete characterization of binary morphisms which preserve Sturmian words and show that infinite words generated by these morphisms are rigid.
@article{JTNB_1993__5_2_221_0,
author = {Filippo Mignosi and Patrice S\'e\'ebold},
title = {Morphismes sturmiens et r\`egles de {Rauzy}},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {221--233},
year = {1993},
publisher = {Universit\'e Bordeaux I},
volume = {5},
number = {2},
zbl = {0797.11029},
mrnumber = {1265903},
language = {fr},
url = {https://jtnb.centre-mersenne.org/item/JTNB_1993__5_2_221_0/}
}
TY - JOUR AU - Filippo Mignosi AU - Patrice Séébold TI - Morphismes sturmiens et règles de Rauzy JO - Journal de théorie des nombres de Bordeaux PY - 1993 SP - 221 EP - 233 VL - 5 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_1993__5_2_221_0/ LA - fr ID - JTNB_1993__5_2_221_0 ER -
Filippo Mignosi; Patrice Séébold. Morphismes sturmiens et règles de Rauzy. Journal de théorie des nombres de Bordeaux, Tome 5 (1993) no. 2, pp. 221-233. https://jtnb.centre-mersenne.org/item/JTNB_1993__5_2_221_0/
[1] , A characterization of the quadratic irrationals, Canad. Math. Bull. 34 (1991), 36-41. | Zbl | MR
[2] , , , , Substitution invariant cutting sequences, Journal de Théorie des Nombres de Bordeaux 5 (1993), 123-137. | Zbl | MR | Numdam
[3] , , Sequences with minimal block growth, Math. Systems Theory 7 (1973), 138-153. | Zbl | MR
[4] , , Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990), 381-400. | Zbl | MR
[5] , , , Determination of [nθ] by its sequence of differences, Canad. Math. Bull. 21 (1978), 441-446. | Zbl
[6] , Sturmian minimal sets, Amer. J. Math 66 (1944), 605-620. | Zbl | MR
[7] , , Symbolic dynamics II - Sturmian trajectories, Amer. J. Math. 62 (1940), 1-42. | Zbl | MR | JFM
[8] , , On continued fractions, substitutions and characteristic sequences, Japan. J. Math. 16 (1990), 287-306. | Zbl | MR
[9] , Problems 149-151, "Problems and Solutions", EATCS Bulletin 32 (1987), 331-333.
[10] , Combinatorics on words, Addison Wesley, 1982. | Zbl | MR
[11] , On the number of factors of Sturmian words, Theoret. Comput. Sci. 82 (1991), 71-84. | Zbl | MR
[12] , Mots infinis en arithmétique, in Automata on infinite words, Nivat, Perrin (Eds), Lecture Notes in Computer Science, Springer-Verlag 192 (1984), 165-171. | Zbl | MR
[13] , Fibonacci morphisms and Sturmian words, Theoret. Comput. Sci. 88 (1991), 365-384. | Zbl | MR
[14] , The geometry of Markoff numbers, Math. Intelligencer 7 (1985), 20-29. | Zbl | MR
[15] , Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull. 19 (1976), 473-482. | Zbl | MR
[16] , Elementary Number Theory, Wolters-Noordhoff, Groningen, 1970. | Zbl | MR