Substitution dynamical systems : algebraic characterization of eigenvalues
Ferenczi, Sébastien ; Mauduit, Christian ; Nogueira, Arnaldo
Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996), p. 519-533 / Harvested from Numdam
@article{ASENS_1996_4_29_4_519_0,
     author = {Ferenczi, S\'ebastien and Mauduit, Christian and Nogueira, Arnaldo},
     title = {Substitution dynamical systems : algebraic characterization of eigenvalues},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {29},
     year = {1996},
     pages = {519-533},
     doi = {10.24033/asens.1746},
     mrnumber = {97b:58085},
     zbl = {0866.11023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1996_4_29_4_519_0}
}
Ferenczi, Sébastien; Mauduit, Christian; Nogueira, Arnaldo. Substitution dynamical systems : algebraic characterization of eigenvalues. Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996) pp. 519-533. doi : 10.24033/asens.1746. http://gdmltest.u-ga.fr/item/ASENS_1996_4_29_4_519_0/

[DEK] M. Dekking, The spectrum of dynamical systems arising from substitutions of constant length (Zeit. Wahrsch. verw. Geb., Vol. 41, 1978, pp. 221-239). | MR 57 #1455 | Zbl 0348.54034

[HOS] B. Host, Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable (Ergodic Th. Dyn. Syst., Vol. 6, 1986, pp. 529-540). | MR 88i:26007 | Zbl 0625.28011

[KEA] M. S. Keane, Interval exchange transformations (Math. Zeitsch., Vol. 141, 1975, pp. 25-31). | MR 50 #10207 | Zbl 0278.28010

[LIV] A. N. Livshits, A sufficient condition for weak mixing of substitutions and stationary adic transformations (Mat. Zametki, Vol. 44, 1988, pp. 785-793, translated in Math. Notes 44, 1988, pp. 920-925). | MR 90c:28027 | Zbl 0713.28011

[LIV-VER] A. N. Livshits and A. M. Vershik, Adic models of ergodic transformations, spectral theory, substitutions, and related topics (Adv. Sov. Mat., Vol. 9, 1992, pp. 185-204). | MR 93i:46131 | Zbl 0770.28013

[MAU] C. Mauduit, Caractérisation des ensembles normaux substitutifs (Inventiones Math., Vol. 95, 1989, pp. 133-147). | MR 90b:11075 | Zbl 0665.10035

[MOS] B. Mosse, Notions de reconnaissabilité pour les substitutions et complexité des suites automatiques (submitted).

[NOG-RUD] A. Nogueira and D. J. Rudolph, Topological weak mixing of interval exchange maps (preprint, Maryland University, 1991).

[PIS] C. Pisot, La répartition modulo 1 et les nombres algébriques (Ann. Sc. Norm. Super. Pisa Cl. Sci., IV Ser., 1938, pp. 205-248). | JFM 64.0994.01 | Numdam | Zbl 0019.15502

[QUE] M. Queffelec, Substitution dynamical systems - Spectral analysis (Lecture Notes in Math., Vol. 1294, 1987, Springer-Verlag). | MR 89g:54094 | Zbl 0642.28013

[SAL] R. Salem, Algebraic numbers and Fourier analysis (Heath Mathematical Monographs, 1963, Heath and Co). | MR 28 #1169 | Zbl 0126.07802

[SOL1] B. Solomyak, Substitutions, adic transformations, and beta-expansions (Contemporary Mat., Vol. 135, 1992, pp. 361-372). | MR 93j:58044 | Zbl 0771.28013

[SOL2] B. Solomyak, On simultaneous action of Markov shift and adic transformation (Adv. Sov. Mat., Vol. 9, 1992, pp. 231-239). | MR 93h:28028 | Zbl 0771.28014

[SOL3] B. Solomyak, On the spectral theory of adic transformations (Adv. Sov. Mat., Vol. 9, 1992, pp. 217-230). | MR 93h:28028 | Zbl 0770.28012

[VEE] W. Veech, Gauss measures for transformations on spaces of interval exchange maps (Annals of Math., Vol. 115, 1982, pp. 201-242). | MR 83g:28036b | Zbl 0486.28014