Abstract
A class of minimal actions of finitely generated abelian groups is constructed. The class contains many non-trivial actions with quasi discrete spectrum and is used to give an ergodic theoretic proof of Weyl's theorem on uniform distribution of polynomials of finitely many variables.
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Abromov, L. M.: Metric automorphisms with quasi discrete spectrum. Izv. Akad. Nauk. SSSR Ser. Mat.26, 513–530 (1962).
Furstenberg, H.: Stationary Processes and Prediction Theory. Princeton: Princeton Univ. Press. 1960.
Hahn, F., andW. Parry: Minimal dynamical systems with quasi discrete spectrum. J. London Math. Soc.40, 309–323 (1965).
Hahn, F.: On affine transformations of compact abelian groups. Amer. J. Math.85, 428–446 (1963).
Hahn, F.: Discrete real time flows with quasi discrete spectra and algebras generated by expq(t). Isr. J. Math.16, 20–37 (1973).
Hoare A. H. M., andW. Parry: Semi-groups of affine transformations. Quart. J. Math.17, 106–111 (1966).
Kurosh, A. G.: The Theory of Groups, Vol. 1. New York: Chelsea. 1960.
Oxtoby, J. C.: Ergodic sets. Bull. Amer. Math. Soc.58, 116–136 (1952).
Parry, W.: Notes on a posthumous paper of F. Hahn. Isr. J. Math.16, 38–45 (1973).
Weyl, H.: Über die Gleichverteilung von Zahlen mod Eins. Math. Ann.77, 313–352 (1916).
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Fellgett, R. A class of flows with quasi discrete spectrum. Monatshefte f#x00FC;r Mathematik 87, 209–228 (1979). https://doi.org/10.1007/BF01303076
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DOI: https://doi.org/10.1007/BF01303076