Email this article On ergodic flows with simple Lebesgue spectrum
- Authors: Prikhod'ko A.A.1,2
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Affiliations:
- Department of Innovations and High Technology, Moscow Institute of Physics and Technology
- Caucasus Mathematical Center, Adyghe State University
- Issue: Vol 211, No 4 (2020)
- Pages: 123-144
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133328
- DOI: https://doi.org/10.4213/sm8147
- ID: 133328
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Abstract
We prove the existence of ergodic flows with invariant probability measure having a Lebesgue spectrum of multiplicity $1$. Bibliography: 15 titles.
About the authors
Aleksandr Alexandrovich Prikhod'ko
Department of Innovations and High Technology, Moscow Institute of Physics and Technology; Caucasus Mathematical Center, Adyghe State University
Email: alexander.a.prikhodko@yandex.ru
Candidate of physico-mathematical sciences, no status
References
- И. П. Корнфельд, Я. Г. Синай, С. В. Фомин, Эргодическая теория, Наука, М., 1980, 384 с.
- A. Katok, J.-P. Thouvenot, “Spectral properties and combinatorial constructions in ergodic theory”, Handbook of dynamical systems, v. 1B, Elsevier B. V., Amsterdam, 2006, 649–743
- M. Lemanczyk, “Spectral theory of dynamical systems”, Encyclopedia of Complexity and System Science, Springer, New York, 2009, 8554–8575
- Д. В. Аносов, “О спектральных кратностях в эргодической теории”, Совр. пробл. матем., 3, МИАН, М., 2003, 3–85
- С. Улам, Нерешeнные математические задачи, Наука, М., 1964, 168 с.
- А. А. Кириллов, “Динамические системы, факторы и представления групп”, УМН, 22:5(137) (1967), 67–80
- А. А. Приходько, “Полиномы Литлвуда и их приложения к спектральной теории динамических систем”, Матем. сб., 204:6 (2013), 135–160
- J. E. Littlewood, “On polynomials $sum^n pm z^m$, $sum^n e^{alpha_m i} z^m$, $z = e^{theta_i}$”, J. London Math. Soc., 41 (1966), 367–376
- T. Erdelyi, “Polynomials with Littlewood-type coefficient constraints”, Approximation theory X. Abstract and classical analysis (St. Louis, MO, 2001), Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 2002, 153–196
- J.-P. Kahane, “Sur les polynômes à coefficient unimodulaires”, Bull. London Math. Soc., 12:5 (1980), 321–342
- А. А. Приходько, “Стохастические конструкции потоков ранга 1”, Матем. сб., 192:12 (2001), 61–92
- J. Bourgain, “On the spectral type of Ornstein's class one transformations”, Israel J. Math., 84:1-2 (1993), 53–63
- D. S. Ornstein, “On the root problem in ergodic theory”, Proceedings of the 6th Berkeley symposium on mathematical statistics and probability (Univ. California, Berkeley, Calif., 1970/1971), v. II, Probability theory, Univ. California Press, Berkeley, CA, 1972, 347–356
- А. Н. Ширяев, Вероятность, Наука, М., 1980, 576 с.
- A. A. Prikhod'ko, Singular Schaeffer–Salem measures of dynamical system origin
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