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Russian Mathematical Surveys, 2008, Volume 63, Issue 2, Pages 221–282
DOI: https://doi.org/10.1070/RM2008v063n02ABEH004515 (Mi rm9171) 		 
This article is cited in 11 scientific papers (total in 11 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
English version PDF (910 kB) Citations (11)
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DOI: https://doi.org/10.1070/RM2008v063n02ABEH004515
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.
Received: 09.01.2008
Russian version:
Uspekhi Matematicheskikh Nauk, 2008, Volume 63, Issue 2(380), Pages 21–84
DOI: https://doi.org/10.4213/rm9171
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: Primary 76F06; Secondary 28A80, 34D45, 35B41, 37B25, 37C70, 37D45, 37G35, 3
Language: English
Original paper language: Russian
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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\paper Mathematical aspects of the theory of development of turbulence in the sense of Landau
\jour Uspekhi Mat. Nauk
\yr 2008
\vol 63
\issue 2(380)
\pages 21--84
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\jour Russian Math. Surveys
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\vol 63
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    • This publication is cited in the following 11 articles:
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    References:95
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