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This article is cited in 7 scientific papers (total in 7 papers)
Weighted averages, uniform distribution, and strict ergodicity
V. V. Kozlov
Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
A circle of problems related to the application of the Riesz and Voronoi summation methods in ergodic theory, number theory, and probability theory is considered. The first digit paradox is discussed, strengthenings of the classical result of Weyl on the uniform distribution of the fractional parts of the values of a polynomial are indicated, and the possibility of sharpening the Birkhoff–Khinchin ergodic theorem is considered. In conclusion, some unsolved problems are listed.
DOI:
https://doi.org/10.4213/rm1679
 Full text:
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English version:
Russian Mathematical Surveys, 2005, 60:6, 1121–1146
Bibliographic databases:
     
UDC:
510.6+519.21
MSC: Primary 40G05, 11K06, 37A30; Secondary 60F15
Received: 17.08.2005
Citation:
V. V. Kozlov, “Weighted averages, uniform distribution, and strict ergodicity”, Uspekhi Mat. Nauk, 60:6(366) (2005), 115–138; Russian Math. Surveys, 60:6 (2005), 1121–1146
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/umn1679https://doi.org/10.4213/rm1679 http://mi.mathnet.ru/eng/umn/v60/i6/p115
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Khryashchev S.M., “Evaluation of Control Times For Continuous Dynamical Polysystems With Control Switchings At Discrete Times”, 2015 International Conference “Stability and Control Processes” in Memory of V.i. Zubov (Scp), eds. Petrosyan L., Zhabko A., IEEE, 2015
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Khryashchev S., “Application of Probabilistic Methods For Research of Polysystems With Switchings in Discrete Times”, Proceedings of 2016 International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy'S Conference), ed. Tkhai V., IEEE, 2016
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Surano F.V., Bongiorno Ch., Zino L., Porfiri M., Rizzo A., “Backbone Reconstruction in Temporal Networks From Epidemic Data”, Phys. Rev. E, 100:4 (2019), 042306
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V. I. Bogachev, “Non-uniform Kozlov–Treschev averagings in the ergodic theorem”, Russian Math. Surveys, 75:3 (2020), 393–425
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