On the relationship between zero entropy and quasi-discrete spectrum for affine transformations

On the relationship between zero entropy and quasi-discrete spectrum for affine transformations
HTML articles powered by AMS MathViewer

Proc. Amer. Math. Soc. 18 (1967), 661-667

DOI: https://doi.org/10.1090/S0002-9939-1967-0212163-2

PDF | Request permission

References

L. M. Abramov, Metric automorphisms with quasi-discrete spectrum, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 513–530 (Russian). MR 0143040
Frank Hahn and William Parry, Minimal dynamical systems with quasi-discrete spectrum, J. London Math. Soc. 40 (1965), 309–323. MR 175107, DOI 10.1112/jlms/s1-40.1.309
A. H. M. Hoare and W. Parry, Semi-groups of affine transformations, Quart. J. Math. Oxford Ser. (2) 17 (1966), 106–111. MR 204614, DOI 10.1093/qmath/17.1.106
H. Hoare and W. Parry, Affine transformations with quasi-discrete spectrum. I, J. London Math. Soc. 41 (1966), 88–96. MR 186750, DOI 10.1112/jlms/s1-41.1.88
R. Robert Laxton and William Parry, On the periodic points of certain automorphisms and a system of polynomial identities, J. Algebra 6 (1967), 388–393. MR 212123, DOI 10.1016/0021-8693(67)90091-9
William Parry, On the coincidence of three invariant $\sigma$-algebras associated with an affine transformation, Proc. Amer. Math. Soc. 17 (1966), 1297–1302. MR 200412, DOI 10.1090/S0002-9939-1966-0200412-5

Topological groups

V. A. Rohlin, Metric properties of endomorphisms of compact commutative groups, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 867–874 (Russian). MR 0168697
V. A. Rohlin, Exact endomorphisms of a Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 499–530 (Russian). MR 0143873
V. A. Rohlin, On the fundamental ideas of measure theory, Mat. Sbornik N.S. 25(67) (1949), 107–150 (Russian). MR 0030584
V. A. Rohlin, New progress in the theory of transformations with invariant measure. , Russian Math. Surveys 15 (1960), no. 4, 1–22. MR 0132155, DOI 10.1070/RM1960v015n04ABEH004095
S. A. Juzvinskiĭ, Metric properties of the endomorphisms of compact groups, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 1295–1328 (Russian). MR 0194588

Modern algebra