On metric properties of substitutions

Mariusz Lemańczyk; Mieczystaw K. Mentzen

Compositio Mathematica (1988)

  • Volume: 65, Issue: 3, page 241-263
  • ISSN: 0010-437X

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Lemańczyk, Mariusz, and Mentzen, Mieczystaw K.. "On metric properties of substitutions." Compositio Mathematica 65.3 (1988): 241-263. <http://eudml.org/doc/89892>.

@article{Lemańczyk1988,
author = {Lemańczyk, Mariusz, Mentzen, Mieczystaw K.},
journal = {Compositio Mathematica},
keywords = {substitutions of constant length; measure-theoretic centralizer of bijective substitutions; dynamical systems; discrete spectrum},
language = {eng},
number = {3},
pages = {241-263},
publisher = {Kluwer Academic Publishers},
title = {On metric properties of substitutions},
url = {http://eudml.org/doc/89892},
volume = {65},
year = {1988},
}

TY - JOUR
AU - Lemańczyk, Mariusz
AU - Mentzen, Mieczystaw K.
TI - On metric properties of substitutions
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 65
IS - 3
SP - 241
EP - 263
LA - eng
KW - substitutions of constant length; measure-theoretic centralizer of bijective substitutions; dynamical systems; discrete spectrum
UR - http://eudml.org/doc/89892
ER -

References

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  2. 2 S. Ferenczi, Systèmes localment de rang un, Ann. Inst. H. Poincaré20 no 1 (1984). Zbl0535.28010MR740249
  3. 3 N. Friedman, Introduction to ergodic theory, Van Nostrand Reinholds Studies no 29, New York (1970). Zbl0212.40004MR435350
  4. 4 H. Fürstenberg, Disjointness in ergodic theory, minimal sets and a problem in diophantine approximation, Math. Syst. Theory1 (1967) 1-49. Zbl0146.28502MR213508
  5. 5 A. del Junco, Transformations with discrete spectrum are stacking transformations, Can. J. Math.28 (1976) 836-839. Zbl0312.47003MR414822
  6. 6 A. del Junco, A transformation with simple spectrum which is not rank one, Can. J. Math.XXIX (1977) 655-663. Zbl0335.28010MR466489
  7. 7 A. del Junco and D.J. Rudolph, On ergodic actions whose self-joinings are graphs, preprint. Zbl0646.60010MR922364
  8. 8 J. King, The commutant is the weak closure of the powers for rank 1 transformations, Erg. Th. Dyn. Syst.6 (1986) 363-384. Zbl0595.47005MR863200
  9. 9 J. King, For mixing transformations rank (Tk) = k · rank (T), Isr. J. Math.56 (1986) 102-122. Zbl0626.47012MR879918
  10. 10 M. Lemańczyk, The centralizer of Morse shifts, Ann. Univ. Clermont-Ferrand4 (1985) 43-56. Zbl0587.28016MR826355
  11. 11 M. Lemańczyk, The rank of regular Morse dynamical systems, Z. Wahr. Verw. Geb.70 (1985) 33-48. Zbl0549.28026MR795787
  12. 12 M. Lemańczyk and A. Sikorski, A class of not local rank one automorphisms arising from continuous substitutions, Prob. Theory and Rel. Fields76 (1987) 421-428. Zbl0611.60002MR917671
  13. 13 D. Newton, Coalescence and spectrum of automorphisms of a Lebesgue space, Z. Wahr. Verw. Geb.19 (1971) 117-122. Zbl0201.38401MR289748
  14. 14 D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979) 129-136. Zbl0425.28012MR527744
  15. 15 M. Queffelec, Contribution á l'etude spectrale de suite arithmétiques, thesis (1984). 
  16. 16 D. Rudolph, The second centralizer of a Bernoulli shifts is just its powers, Isr. J. Math.29 (1978) 167-178. Zbl0375.28006MR485401

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