@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://www.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://www.numdam.org/item/AIHPB_2002__38_2_155_0/ LA - en ID - AIHPB_2002__38_2_155_0 ER -
Kwiatkowski, Jan; Lacroix, Yves. Finite rank transformation and weak closure theorem. Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 2, pp. 155-192. http://www.numdam.org/item/AIHPB_2002__38_2_155_0/
[1] Smorodinsky's conjecture on rank 1 mixing, Proc. Amer. Math. Soc. 126 (1998) 739-744. | MR | Zbl
,[2] Suites algébriques, automates et substitutions, Bull. Soc. Math. France 108 (1980) 401-419. | Numdam | MR | Zbl
, , , ,[3] A transformation with simple spectrum which is not rank one, Canad. J. Math. 29 (1977) 655-663. | MR | Zbl
,[4] Systèmes localement de rang un, Ann. Inst. Henri Poincaré, Probab. Stat. 20 (1984) 35-51. | Numdam | MR | Zbl
,[5] Systèmes de rang un gauche, Ann. Inst. Henri Poincaré, Probab. Stat. 21 (1985) 177-186. | Numdam | MR | Zbl
,[6] Systems of finite rank, Colloq. Math. 73 (1) (1997) 35-65. | MR | Zbl
,[7] Rank and spectral multiplicity, Stud. Math. 102 (2) (1992) 121-144. | MR | Zbl
, ,[8] Rank, covering number and simple spectrum, J. d'Analyse Math. 66 (1995) 185-216. | MR | Zbl
, ,[9] On the multiplicity function of ergodic group extensions of rotations, Studia Math. 102 (1992) 157-174. | Zbl
, , , ,[10] The commutant is the weak closure of the powers, for rank-1 transformations, Ergodic Theory Dynam. Systems 6 (1986) 363-385. | MR | Zbl
,[11] Joining - rank and the structure of finite rank mixing transformations, J. d'Analyse Math. 51 (1988) 182-227. | Zbl
,[12] A lower bound for the rank of mixing transformations, Israel J. Math. 59 (1987) 377-380. | MR | Zbl
,[13] 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] On the multiplicity function of ergodic group extensions, Studia Math. 116 (1995) 207-215. | MR | Zbl
, ,[16] 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] Coalescence of circle extensions of measure-preserving transformations, Ergodic Theory Dynam. Systems 12 (1992) 769-789. | MR | Zbl
, , ,[19] 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] On canonical factors of ergodic dynamical systems, J. London Math. Soc. 2 19 (1979) 129-136. | MR | Zbl
,[22] Compact abelian group extensions of discrete dynamical systems, Z. Wahr. Verv. Geb. 13 (1969) 95-113. | MR | Zbl
,[23] On metric isomorphism of Morse dynamical systems, Studia Math. 84 (1986) 247-267. | MR | Zbl
,[24] K-fold mixing lifts to weakly mixing isometric extensions, Ergodic Theory Dynam. Systems 5 (1985) 445-447. | MR | Zbl
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