Substitution dynamical systems : algebraic characterization of eigenvalues

Sébastien Ferenczi; Christian Mauduit; Arnaldo Nogueira

Annales scientifiques de l'École Normale Supérieure (1996)

  • Volume: 29, Issue: 4, page 519-533
  • ISSN: 0012-9593

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Ferenczi, Sébastien, Mauduit, Christian, and Nogueira, Arnaldo. "Substitution dynamical systems : algebraic characterization of eigenvalues." Annales scientifiques de l'École Normale Supérieure 29.4 (1996): 519-533. <http://eudml.org/doc/82415>.

@article{Ferenczi1996,
author = {Ferenczi, Sébastien, Mauduit, Christian, Nogueira, Arnaldo},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {automatic sequences; Pisot numbers; eigenvalues of dynamical systems; primitive substitution; weakly mixing},
language = {eng},
number = {4},
pages = {519-533},
publisher = {Elsevier},
title = {Substitution dynamical systems : algebraic characterization of eigenvalues},
url = {http://eudml.org/doc/82415},
volume = {29},
year = {1996},
}

TY - JOUR
AU - Ferenczi, Sébastien
AU - Mauduit, Christian
AU - Nogueira, Arnaldo
TI - Substitution dynamical systems : algebraic characterization of eigenvalues
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1996
PB - Elsevier
VL - 29
IS - 4
SP - 519
EP - 533
LA - eng
KW - automatic sequences; Pisot numbers; eigenvalues of dynamical systems; primitive substitution; weakly mixing
UR - http://eudml.org/doc/82415
ER -

References

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  1. [DEK] M. DEKKING, The spectrum of dynamical systems arising from substitutions of constant length (Zeit. Wahrsch. verw. Geb., Vol. 41, 1978, pp. 221-239). Zbl0348.54034MR57 #1455
  2. [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). Zbl0625.28011MR88i:26007
  3. [KEA] M. S. KEANE, Interval exchange transformations (Math. Zeitsch., Vol. 141, 1975, pp. 25-31). Zbl0278.28010MR50 #10207
  4. [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). Zbl0713.28011MR90c:28027
  5. [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). Zbl0770.28013MR93i:46131
  6. [MAU] C. MAUDUIT, Caractérisation des ensembles normaux substitutifs (Inventiones Math., Vol. 95, 1989, pp. 133-147). Zbl0665.10035MR90b:11075
  7. [MOS] B. MOSSE, Notions de reconnaissabilité pour les substitutions et complexité des suites automatiques (submitted). 
  8. [NOG-RUD] A. NOGUEIRA and D. J. RUDOLPH, Topological weak mixing of interval exchange maps (preprint, Maryland University, 1991). 
  9. [PIS] C. PISOT, La répartition modulo 1 et les nombres algébriques (Ann. Sc. Norm. Super. Pisa Cl. Sci., IV Ser., 1938, pp. 205-248). Zbl0019.15502JFM64.0994.01
  10. [QUE] M. QUEFFELEC, Substitution dynamical systems - Spectral analysis (Lecture Notes in Math., Vol. 1294, 1987, Springer-Verlag). Zbl0642.28013MR89g:54094
  11. [SAL] R. SALEM, Algebraic numbers and Fourier analysis (Heath Mathematical Monographs, 1963, Heath and Co). Zbl0126.07802MR28 #1169
  12. [SOL1] B. SOLOMYAK, Substitutions, adic transformations, and beta-expansions (Contemporary Mat., Vol. 135, 1992, pp. 361-372). Zbl0771.28013MR93j:58044
  13. [SOL2] B. SOLOMYAK, On simultaneous action of Markov shift and adic transformation (Adv. Sov. Mat., Vol. 9, 1992, pp. 231-239). Zbl0771.28014MR93h:28028
  14. [SOL3] B. SOLOMYAK, On the spectral theory of adic transformations (Adv. Sov. Mat., Vol. 9, 1992, pp. 217-230). Zbl0770.28012MR93h:28028
  15. [VEE] W. VEECH, Gauss measures for transformations on spaces of interval exchange maps (Annals of Math., Vol. 115, 1982, pp. 201-242). Zbl0486.28014MR83g:28036b

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