Spectral properties of G-symbolic Morse shifts

Jan Kwiatkowski; Andrzej Sikorski

Bulletin de la Société Mathématique de France (1987)

  • Volume: 115, page 19-33
  • ISSN: 0037-9484

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Kwiatkowski, Jan, and Sikorski, Andrzej. "Spectral properties of G-symbolic Morse shifts." Bulletin de la Société Mathématique de France 115 (1987): 19-33. <http://eudml.org/doc/87528>.

@article{Kwiatkowski1987,
author = {Kwiatkowski, Jan, Sikorski, Andrzej},
journal = {Bulletin de la Société Mathématique de France},
keywords = {G-symbolic Morse dynamical systems; spectral properties of Morse shifts over finite Abelian groups; shift transformation; Morse sequences; maximal spectral multiplicity},
language = {eng},
pages = {19-33},
publisher = {Société mathématique de France},
title = {Spectral properties of G-symbolic Morse shifts},
url = {http://eudml.org/doc/87528},
volume = {115},
year = {1987},
}

TY - JOUR
AU - Kwiatkowski, Jan
AU - Sikorski, Andrzej
TI - Spectral properties of G-symbolic Morse shifts
JO - Bulletin de la Société Mathématique de France
PY - 1987
PB - Société mathématique de France
VL - 115
SP - 19
EP - 33
LA - eng
KW - G-symbolic Morse dynamical systems; spectral properties of Morse shifts over finite Abelian groups; shift transformation; Morse sequences; maximal spectral multiplicity
UR - http://eudml.org/doc/87528
ER -

References

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  1. [1] BAXTER (J. R.). — A class of ergodic transformations having simple spectra, P.A.M.S., Vol. 27, 1971, pp. 275-279. Zbl0206.06404MR43 #2187
  2. [2] COQUET (J.), KAMAE (T.) et MENDES-FRANCE (M.). — Sur la mesure spectrale de certaines suites arithmétiques, Bull. Soc. Math. France, Vol. 105, 1977, pp. 369-384. Zbl0383.10035MR57 #12439
  3. [3] DEL JUNCO (A.). — A transformation with simple spectrum which is not rank one, Can. J. Math., Vol. 29, No. 3, 1977, pp. 653-663. Zbl0335.28010MR57 #6367
  4. [4] GOODSON (G. R.). — On the spectral multiplicity of a class of finite rank transformation, preprint, 1984. 
  5. [5] KAKUTANI (S.). — Strictly ergodic symbolic dynamical systems, Proc. 6th Berkeley Symp., Vol. 2, pp. 319-326. Zbl0262.28014MR53 #8383
  6. [6] KEANE (M.). — Generalized Morse sequences, Z. Wahr. verw. Geb., Vol. 10, 1968, pp. 335-353. Zbl0162.07201MR39 #406
  7. [7] KEANE (M.). — Strongly mixing g-measures, Inventiones Math., Vol. 16, No. 4, 1972, pp. 309-324. Zbl0241.28014MR46 #9295
  8. [8] KWIATKOWSKI (J.). — Spectral isomorphism of Morse dynamical systems, Bull. Acad. Pol. Sc., serie sc. math., Vol. XXIX, No. 3-4, 1981, pp. 105-114. Zbl0496.28019MR83g:28033
  9. [9] KWIATKOWSKI (J.). — Isomorphism of regular Morse dynamical systems induced by arbitrary blocks, Studia Math., Vol. 84, No. 3 (to appear). Zbl0674.58023MR88g:28020a
  10. [10] LEMANCZYK (M.). — The centralizer of Morse shifts. Zbl0587.28016
  11. [11] MARTIN (J. C.). — Generalized Morse sequences on n-symbols, P.A.M.S., Vol. 54, 1976, pp. 379-383. Zbl0317.54054MR52 #11880
  12. [12] MARTIN (J. C.). — The structure of generalized Morse minimal sets on n-symbols, P.A.M.S., Vol. 2, 1977, pp. 343-355. Zbl0375.28010MR57 #3352
  13. [13] QUEFFELEC (M.). — Mesures spectrales associées à certaines suites arithmétiques, Bull. Soc. Math. France, Vol. 107, 1979, pp. 385-421. Zbl0435.42007MR81c:10071
  14. [14] QUEFFELEC (M.). — Contribution à l'étude spectrale de suites arithmétiques, Thèse, 1984. 
  15. [15] PARRY (W.). — Topics in ergodic theory, Cambridge, University Press, 1981. Zbl0449.28016MR83a:28018
  16. [16] ROBINSON (E. R.). — Ergodic measure preserving transformations with arbitrary finite spectral multiplicity, Preprint, University of Maryland, 1982. 

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