Most monothetic extensions are rank-1

A. Iwanik; J. Serafin

Colloquium Mathematicae (1993)

  • Volume: 66, Issue: 1, page 63-76
  • ISSN: 0010-1354

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Iwanik, A., and Serafin, J.. "Most monothetic extensions are rank-1." Colloquium Mathematicae 66.1 (1993): 63-76. <http://eudml.org/doc/210235>.

@article{Iwanik1993,
author = {Iwanik, A., Serafin, J.},
journal = {Colloquium Mathematicae},
keywords = {Anzai-cocyle; -extensions; ergodic automorphism},
language = {eng},
number = {1},
pages = {63-76},
title = {Most monothetic extensions are rank-1},
url = {http://eudml.org/doc/210235},
volume = {66},
year = {1993},
}

TY - JOUR
AU - Iwanik, A.
AU - Serafin, J.
TI - Most monothetic extensions are rank-1
JO - Colloquium Mathematicae
PY - 1993
VL - 66
IS - 1
SP - 63
EP - 76
LA - eng
KW - Anzai-cocyle; -extensions; ergodic automorphism
UR - http://eudml.org/doc/210235
ER -

References

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  1. [A] H. Anzai, Ergodic skew product transformations on the torus, Osaka Math. J. 3 (1951), 83-99. Zbl0043.11203
  2. [B] L. Baggett, On functions that are trivial cocycles for a set of irrationals, Proc. Amer. Math. Soc. 104 (1988), 1212-1217. Zbl0692.28008
  3. [Ba] J. R. Baxter, A class of ergodic transformations having simple spectrum, ibid. 27 (1971), 275-279. Zbl0206.06404
  4. P. Gabriel, M. Lemańczyk et P. Liardet, Ensemble d'invariants pour les produits croisés de Anzai, Suppl. Bull. Soc. Math. France 119 (3) (1991), Mém. 47. Zbl0754.28011
  5. [J-P] R. Jones and W. Parry, Compact abelian group extensions of dynamical systems II, Compositio Math. 25 (1972), 135-147. Zbl0243.54039
  6. [J] A. del Junco, Transformations with discrete spectrum are stacking transformations, Canad. J. Math. 28 (1976), 836-839. Zbl0312.47003
  7. [K-S] A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Uspekhi Mat. Nauk 22 (1967), 81-106 (in Russian); English transl.: Russian Math. Surveys 22 (1967), 77-102. Zbl0172.07202
  8. [P] B. J. Pettis, On continuity and openness of homomorphisms in topological groups, Ann. of Math. 52 (1950), 293-308. Zbl0037.30501
  9. [R1] E. A. Robinson, Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Invent. Math. 72 (1983), 299-314. Zbl0519.28008
  10. [R2] E. A. Robinson, Non-abelian extensions have nonsimple spectrum, Compositio Math. 65 (1988), 155-170. Zbl0641.28011
  11. [Ru] D. J. Rudolph, n and n cocycle extensions and complementary algebras, Ergodic Theory Dynamical Systems 6 (1986), 583-599. 

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