Dynamical representations in nilmanifolds
Compositio Mathematica, Volume 26 (1973) no. 2, p. 159-174
@article{CM_1973__26_2_159_0,
     author = {Parry, William},
     title = {Dynamical representations in nilmanifolds},
     journal = {Compositio Mathematica},
     publisher = {Noordhoff International Publishing},
     volume = {26},
     number = {2},
     year = {1973},
     pages = {159-174},
     zbl = {0256.22013},
     mrnumber = {320277},
     language = {en},
     url = {http://www.numdam.org/item/CM_1973__26_2_159_0}
}
Parry, William. Dynamical representations in nilmanifolds. Compositio Mathematica, Volume 26 (1973) no. 2, pp. 159-174. http://www.numdam.org/item/CM_1973__26_2_159_0/

W. Parry [1] Metric classification of ergodic nilflows and unipotent affines, Amer. J. Math. 93 (1971) 819-828. | MR 284567 | Zbl 0222.22010

J. Von Neumann [2] Zur Operatorenmethode in der Klassischen Mechanik, Ann. of Math. 33 (1932) 587-642. | JFM 58.1270.04 | MR 1503078 | Zbl 0005.12203

P.R. Halmos and J. Von Neumann [3] Operator methods in classical mechanics II, Ann. of Math. (43) (1942) 332-350. | MR 6617 | Zbl 0063.01888

L.M. Abramov [4] Metric automorphisms with quasi-discrete spectrum, Izv. Akad. Nauk. SSSR. 26. (1962) 513-530 ≡ A.M.S. Transl. Ser. 2. 39 (1964) 37-56. | Zbl 0154.15704

F. Hahn and W. Parry [5] Minimal dynamical systems with quasidiscrete spectrum, J.L.M.S. 40 (1965) 309-323. | MR 175107 | Zbl 0132.36001

Ja G. Sinai [6] Weak isomorphism of transformations with invariant measure, Mat. Sbom. 63 (1964) 23-42. (In Russian). | MR 161961

D. Ornstein [7] Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4. (1970) 337-352. | MR 257322 | Zbl 0197.33502

D. Ornstein [8] Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5. (1971) 339-348. | MR 274716 | Zbl 0227.28014

D. Ornstein [9] Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math. 5. (1971) 349-364. | MR 274717 | Zbl 0227.28015

A. Malcev [10] On a class of homogeneous spaces, Izv. Akad. Nauk. SSSR. 13. (1949) 9-32. (In Russian). | MR 28842 | Zbl 0034.01701

H. Furstenberg [11] Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation, Math. Systems. Th. 1. (1967) 1-49. | MR 213508 | Zbl 0146.28502

R. Ellis [12] Distal transformation groups, Pac. J. Math. 8. (1958) 401-405. | MR 101283 | Zbl 0092.39702

W. Parry [13] Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math. 91 (1969) 755-771. | MR 260975 | Zbl 0183.51503

A. Weil [14] L'intégration dans les groupes topologiques et ses applications, Deuxième édition. Hermann. Paris. 1953. | JFM 66.1205.02

W. Parry [15] Compact abelian group extensions of discrete dynamical systems, Z. Wahrscheinlichkeitstheorie verw. Geb. 13. (1969). 95-113. | MR 260976 | Zbl 0184.26901

V.A. Rohlin [16] On the entropy of a metric automorphism, Dokl. Akad. Nauk. SSSR. 124. (1959). 980-983. (In Russian). | MR 103258 | Zbl 0096.31405

F. Hahn and W. Parry [17] Some characteristic properties of dynamical systems with quasi-discrete spectra, Math. Systems. Th. 2. (1968) 179-190. | MR 230877 | Zbl 0167.32902

J. Cigler [18] Invariant σ-algebras on locally compact abelian groups, Proc. Nederl. Akad. Wet. Ser. A. 70. (1967) 375-377. | Zbl 0186.46403