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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 2(380), Pages 21–84 (Mi umn9171)  

This article is cited in 8 scientific papers (total in 8 papers)

Mathematical aspects of the theory of development of turbulence in the sense of Landau

A. Yu. Kolesova, N. Kh. Rozovb, V. A. Sadovnichiib

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University

Abstract: This paper contains some rigorous mathematical results related to the theory of development of turbulence in the sense of Landau. In diverse areas of the natural sciences, specific examples of non-linear dynamical systems are considered (including E. Hopf's classical example) whose attractors turn out to be invariant tori of arbitrarily high dimension under an appropriate change of parameters. The investigation of these examples enables us to give a rigorous meaning to the notion of a ‘turbulent attractor’ in some cases and to reveal the main properties of such an attractor, notable among which are its fractal property and its infinite dimensionality.

DOI: https://doi.org/10.4213/rm9171

Full text: PDF file (1108 kB)
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English version:
Russian Mathematical Surveys, 2008, 63:2, 221–282

Bibliographic databases:

UDC: 517.957
MSC: Primary 76F06; Secondary 28A80, 34D45, 35B41, 37B25, 37C70, 37D45, 37G35, 3
Received: 09.01.2008

Citation: A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “Mathematical aspects of the theory of development of turbulence in the sense of Landau”, Uspekhi Mat. Nauk, 63:2(380) (2008), 21–84; Russian Math. Surveys, 63:2 (2008), 221–282

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Kolesov, N. Kh. Rozov, “On the definition of ‘chaos’”, Russian Math. Surveys, 64:4 (2009), 701–744  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. E. S. Kokuikin, A. N. Kulikov, “Tsikly i tory delovoi aktivnosti v odnoi matematicheskoi modeli makroekonomiki”, Model. i analiz inform. sistem, 16:4 (2009), 86–95  mathnet  elib
    3. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Finite-dimensional models of diffusion chaos”, Comput. Math. Math. Phys., 50:5 (2010), 816–830  mathnet  crossref  adsnasa  isi  elib  elib
    4. Kulikov A.N., “Landau-Hopf scenario of passage to turbulence in some problems of elastic stability theory”, Differ. Equ., 48:9 (2012), 1258–1271  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    5. A. S. Bobok, S. D. Glyzin, “Avtokolebaniya reshetok nelineinykh elementov v opyte Skotta”, Model. i analiz inform. sistem, 19:5 (2012), 56–68  mathnet
    6. Nesterov P.N., Malozemova D.V., Bobok A.S., Kubyshkin E.P., Glyzin S.D., Gorchakova E.V., Kaschenko S.A., “O rabote seminara nelineinaya dinamika”, Modelirovanie i analiz informatsionnykh sistem, 19:3 (2012), 142–150  mathnet  mathscinet  elib
    7. A. P. Kuznetsov, S. P. Kuznetsov, L. V. Tyuryukina, I. R. Sataev, “Stsenarii Landau–Khopfa v ansamble vzaimodeistvuyuschikh ostsillyatorov”, Nelineinaya dinam., 8:5 (2012), 863–873  mathnet
    8. S. D. Glyzin, “Razmernostnye kharakteristiki diffuzionnogo khaosa”, Model. i analiz inform. sistem, 20:1 (2013), 30–51  mathnet
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