References
J. P. Conze,Équirépartition et ergodicité de transformations cylindriques, preprint (Université de Rennes, 1976).
H. Furstenberg, Strict ergodicity and transformations of the torus,Amer. J. Math.,88 (1961), 573–601.
H. Kesten, On a conjecture of Erdős and Szüsz related to uniform distribution mod 1,Acta Arith.,12 (1966), 193–212.
A. Ya. Khinchin,Continued Fractions, University of Chicago Press (Chicago, 1964).
L. Kuipers andH. Niederreiter,Uniform Distribution of Sequences, John Wiley and Sons (New York, 1974).
J. Lesca, Sur la répartition modulo 1 des suites(nα), Seminaire Delange-Pisot-Poitou (theórie des nombres) 8e annee (1966/67), no. 2.
E. Sataev, On the number of invariant measures for flows on orientable surfaces,Izv. Akad. Nauk. USSR,9 (1975), 813–830.
K. Schmidt,Cohomology and skew products of ergodic transformations, preprint (University of Warwick, 1974).
K. Schmidt,A cylinder flow arising from irregularity of distribution, preprint (University of Warwick, 1975).
W. A. Veech, Strict ergodicity in zero-dimensional dynamical systems and the Kronecker-Weyl theorem mod 2,Trans. Amer. Math. Soc.,140 (1969), 1–33.
W. A. Veech, Well distributed sequences of integers,Trans. Amer Math. Soc.,161 (1971), 63–70.
W. A. Veech, Topological dynamics,Bull. Amer. Math. Soc.,83 (1977), 775–830.
T. Vijayaraghavan, On the fractional parts of powers of a number IV,J. Indian Math. Soc.,12 (1948), 33–39.
H. Weyl, Über die Gleichverteilung von Zahlen mod Eins,Math. Ann.,77 (1916), 313–352.
J. P. Conze andM. Keane,Ergodicite d'un flot cylindrique, preprint (Université de Rennes).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stewart, M. Irregularities of uniform distribution. Acta Mathematica Academiae Scientiarum Hungaricae 37, 185–221 (1981). https://doi.org/10.1007/BF01904883
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01904883