Dynamical representations in nilmanifolds

William Parry

Compositio Mathematica (1973)

  • Volume: 26, Issue: 2, page 159-174
  • ISSN: 0010-437X

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Parry, William. "Dynamical representations in nilmanifolds." Compositio Mathematica 26.2 (1973): 159-174. <http://eudml.org/doc/89160>.

@article{Parry1973,
author = {Parry, William},
journal = {Compositio Mathematica},
language = {eng},
number = {2},
pages = {159-174},
publisher = {Noordhoff International Publishing},
title = {Dynamical representations in nilmanifolds},
url = {http://eudml.org/doc/89160},
volume = {26},
year = {1973},
}

TY - JOUR
AU - Parry, William
TI - Dynamical representations in nilmanifolds
JO - Compositio Mathematica
PY - 1973
PB - Noordhoff International Publishing
VL - 26
IS - 2
SP - 159
EP - 174
LA - eng
UR - http://eudml.org/doc/89160
ER -

References

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  1. W. Parry [1] Metric classification of ergodic nilflows and unipotent affines, Amer. J. Math.93 (1971) 819-828. Zbl0222.22010MR284567
  2. J. Von Neumann [2] Zur Operatorenmethode in der Klassischen Mechanik, Ann. of Math.33 (1932) 587-642. Zbl0005.12203MR1503078JFM58.1270.04
  3. P.R. Halmos and J. Von Neumann [3] Operator methods in classical mechanics II, Ann. of Math. (43) (1942) 332-350. Zbl0063.01888MR6617
  4. 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. Zbl0154.15704
  5. F. Hahn and W. Parry [5] Minimal dynamical systems with quasidiscrete spectrum, J.L.M.S.40 (1965) 309-323. Zbl0132.36001MR175107
  6. Ja G. Sinai [6] Weak isomorphism of transformations with invariant measure, Mat. Sbom.63 (1964) 23-42. (In Russian). MR161961
  7. D. Ornstein [7] Bernoulli shifts with the same entropy are isomorphic, Advances in Math.4. (1970) 337-352. Zbl0197.33502MR257322
  8. D. Ornstein [8] Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math.5. (1971) 339-348. Zbl0227.28014MR274716
  9. D. Ornstein [9] Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math.5. (1971) 349-364. Zbl0227.28015MR274717
  10. A. Malcev [10] On a class of homogeneous spaces, Izv. Akad. Nauk. SSSR.13. (1949) 9-32. (In Russian). Zbl0034.01701MR28842
  11. H. Furstenberg [11] Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation, Math. Systems. Th.1. (1967) 1-49. Zbl0146.28502MR213508
  12. R. Ellis [12] Distal transformation groups, Pac. J. Math.8. (1958) 401-405. Zbl0092.39702MR101283
  13. W. Parry [13] Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math.91 (1969) 755-771. Zbl0183.51503MR260975
  14. A. Weil [14] L'intégration dans les groupes topologiques et ses applications, Deuxième édition. Hermann. Paris. 1953. JFM66.1205.02
  15. W. Parry [15] Compact abelian group extensions of discrete dynamical systems, Z. Wahrscheinlichkeitstheorie verw. Geb.13. (1969). 95-113. Zbl0184.26901MR260976
  16. V.A. Rohlin [16] On the entropy of a metric automorphism, Dokl. Akad. Nauk. SSSR.124. (1959). 980-983. (In Russian). Zbl0096.31405MR103258
  17. F. Hahn and W. Parry [17] Some characteristic properties of dynamical systems with quasi-discrete spectra, Math. Systems. Th.2. (1968) 179-190. Zbl0167.32902MR230877
  18. J. Cigler [18] Invariant σ-algebras on locally compact abelian groups, Proc. Nederl. Akad. Wet. Ser. A.70. (1967) 375-377. Zbl0186.46403

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