Finite rank transformation and weak closure theorem

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1. [1] T. Adams, Smorodinsky's conjecture on rank 1 mixing, Proc. Amer. Math. Soc.126 (1998) 739-744. Zbl0906.28006MR1443143
2. [2] G. Christol, T. Kamae, M. Mendès France, G. Rauzy, Suites algébriques, automates et substitutions, Bull. Soc. Math. France108 (1980) 401-419. Zbl0472.10035MR614317
3. [3] A. del Junco, A transformation with simple spectrum which is not rank one, Canad. J. Math.29 (1977) 655-663. Zbl0335.28010MR466489
4. [4] S. Ferenczi, Systèmes localement de rang un, Ann. Inst. Henri Poincaré, Probab. Stat.20 (1984) 35-51. Zbl0535.28010MR740249
5. [5] S. Ferenczi, Systèmes de rang un gauche, Ann. Inst. Henri Poincaré, Probab. Stat.21 (1985) 177-186. Zbl0575.28013MR798894
6. [6] S. Ferenczi, Systems of finite rank, Colloq. Math.73 (1) (1997) 35-65. Zbl0883.28014MR1436950
7. [7] S. Ferenczi, J. Kwiatkowski, Rank and spectral multiplicity, Stud. Math.102 (2) (1992) 121-144. Zbl0809.28013MR1169282
8. [8] I. Filipowicz, J. Kwiatkowski, Rank, covering number and simple spectrum, J. d'Analyse Math.66 (1995) 185-216. Zbl0849.28008MR1370350
9. [9] G. Goodson, J. Kwiatkowski, P. Liardet, M. Lemaǹczyk, On the multiplicity function of ergodic group extensions of rotations, Studia Math.102 (1992) 157-174. Zbl0830.28009
10. [10] J. King, The commutant is the weak closure of the powers, for rank-1 transformations, Ergodic Theory Dynam. Systems6 (1986) 363-385. Zbl0595.47005MR863200
11. [11] J. King, Joining – rank and the structure of finite rank mixing transformations, J. d'Analyse Math.51 (1988) 182-227. Zbl0665.28010
12. [12] J. King, A lower bound for the rank of mixing transformations, Israel J. Math.59 (1987) 377-380. Zbl0647.28012MR920501
13. [13] J. Kwiatkowski, Inverse limit of M-cocycles and applications, Funda. Math.157 (1998) 261-276. Zbl0918.28016MR1636893
14. [14] Kwiatkowski J., Lacroix Y., Morse extensions of rank 1 systems, Prepint, U.B.O. No 04-1998, http://gauss.univ-brest.fr/recherche/prepub/1998.html. 
15. [15] J. Kwiatkowski, M Lemańczyk, On the multiplicity function of ergodic group extensions, Studia Math.116 (1995) 207-215. Zbl0857.28012MR1360702
16. [16] M. Lemańczyk, Toeplitz Z2-extensions, Ann. Inst. Henri Poincaré24 (1988) 1-43. Zbl0647.28013MR937955
17. [17] Lemańczyk M., Liardet P., Coalescence of Anzai skew product, unpublished preprint. Zbl0754.28011
18. [18] M. Lemańczyk, P. Liardet, J.P. Thouvenot, Coalescence of circle extensions of measure-preserving transformations, Ergodic Theory Dynam. Systems12 (1992) 769-789. Zbl0785.58030MR1200343
19. [19] M. Lemańczyk, M. Mentzen, Compact subgroups in the centralizer of natural factors of an ergodic group extension of a rotation determine all factors, Ergodic Theory Dynam. Systems10 (1990) 763-776. Zbl0725.54030MR1091425
20. [20] Mentzen M., Thesis, Preprint no 2/89, Nicholas Copernicus University, Toruń (1989). 
21. [21] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 219 (1979) 129-136. Zbl0425.28012MR527744
22. [22] W. Parry, Compact abelian group extensions of discrete dynamical systems, Z. Wahr. Verv. Geb.13 (1969) 95-113. Zbl0184.26901MR260976
23. [23] T. Rojek, On metric isomorphism of Morse dynamical systems, Studia Math.84 (1986) 247-267. Zbl0657.28011MR877081
24. [24] D.J. Rudolph, K-fold mixing lifts to weakly mixing isometric extensions, Ergodic Theory Dynam. Systems5 (1985) 445-447. Zbl0594.28015MR805841