Finite rank transformation and weak closure theorem
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 2, pp. 155-192. 
@article{AIHPB_2002__38_2_155_0,
     author = {Kwiatkowski, Jan and Lacroix, Yves},
     title = {Finite rank transformation and weak closure theorem},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {155--192},
     publisher = {Elsevier},
     volume = {38},
     number = {2},
     year = {2002},
     mrnumber = {1899109},
     zbl = {01751666},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2002__38_2_155_0/}
}
TY  - JOUR
AU  - Kwiatkowski, Jan
AU  - Lacroix, Yves
TI  - Finite rank transformation and weak closure theorem
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2002
SP  - 155
EP  - 192
VL  - 38
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/item/AIHPB_2002__38_2_155_0/
LA  - en
ID  - AIHPB_2002__38_2_155_0
ER  - 
%0 Journal Article
%A Kwiatkowski, Jan
%A Lacroix, Yves
%T Finite rank transformation and weak closure theorem
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2002
%P 155-192
%V 38
%N 2
%I Elsevier
%U http://archive.numdam.org/item/AIHPB_2002__38_2_155_0/
%G en
%F AIHPB_2002__38_2_155_0
Kwiatkowski, Jan; Lacroix, Yves. Finite rank transformation and weak closure theorem. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 2, pp. 155-192. http://archive.numdam.org/item/AIHPB_2002__38_2_155_0/

[1] T. Adams, Smorodinsky's conjecture on rank 1 mixing, Proc. Amer. Math. Soc. 126 (1998) 739-744. | MR | Zbl

[2] G. Christol, T. Kamae, M. Mendès France, G. Rauzy, Suites algébriques, automates et substitutions, Bull. Soc. Math. France 108 (1980) 401-419. | Numdam | MR | Zbl

[3] A. Del Junco, A transformation with simple spectrum which is not rank one, Canad. J. Math. 29 (1977) 655-663. | MR | Zbl

[4] S. Ferenczi, Systèmes localement de rang un, Ann. Inst. Henri Poincaré, Probab. Stat. 20 (1984) 35-51. | Numdam | MR | Zbl

[5] S. Ferenczi, Systèmes de rang un gauche, Ann. Inst. Henri Poincaré, Probab. Stat. 21 (1985) 177-186. | Numdam | MR | Zbl

[6] S. Ferenczi, Systems of finite rank, Colloq. Math. 73 (1) (1997) 35-65. | MR | Zbl

[7] S. Ferenczi, J. Kwiatkowski, Rank and spectral multiplicity, Stud. Math. 102 (2) (1992) 121-144. | MR | Zbl

[8] I. Filipowicz, J. Kwiatkowski, Rank, covering number and simple spectrum, J. d'Analyse Math. 66 (1995) 185-216. | MR | Zbl

[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. | Zbl

[10] J. King, The commutant is the weak closure of the powers, for rank-1 transformations, Ergodic Theory Dynam. Systems 6 (1986) 363-385. | MR | Zbl

[11] J. King, Joining - rank and the structure of finite rank mixing transformations, J. d'Analyse Math. 51 (1988) 182-227. | Zbl

[12] J. King, A lower bound for the rank of mixing transformations, Israel J. Math. 59 (1987) 377-380. | MR | Zbl

[13] J. Kwiatkowski, Inverse limit of M-cocycles and applications, Funda. Math. 157 (1998) 261-276. | MR | Zbl

[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] J. Kwiatkowski, M Lemańczyk, On the multiplicity function of ergodic group extensions, Studia Math. 116 (1995) 207-215. | MR | Zbl

[16] M. Lemańczyk, Toeplitz Z2-extensions, Ann. Inst. Henri Poincaré 24 (1988) 1-43. | Numdam | MR | Zbl

[17] Lemańczyk M., Liardet P., Coalescence of Anzai skew product, unpublished preprint.

[18] M. Lemańczyk, P. Liardet, J.P. Thouvenot, Coalescence of circle extensions of measure-preserving transformations, Ergodic Theory Dynam. Systems 12 (1992) 769-789. | MR | Zbl

[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. Systems 10 (1990) 763-776. | MR | Zbl

[20] Mentzen M., Thesis, Preprint no 2/89, Nicholas Copernicus University, Toruń (1989).

[21] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 2 19 (1979) 129-136. | MR | Zbl

[22] W. Parry, Compact abelian group extensions of discrete dynamical systems, Z. Wahr. Verv. Geb. 13 (1969) 95-113. | MR | Zbl

[23] T. Rojek, On metric isomorphism of Morse dynamical systems, Studia Math. 84 (1986) 247-267. | MR | Zbl

[24] D.J. Rudolph, K-fold mixing lifts to weakly mixing isometric extensions, Ergodic Theory Dynam. Systems 5 (1985) 445-447. | MR | Zbl