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Visualization of the simplest scenarios of ideal turbulence. (English. Ukrainian original) Zbl 1448.76092

J. Math. Sci., New York 247, No. 2, 223-237 (2020); translation from Neliniĭni Kolyvannya 22, No. 1, 3-17 (2019).
Summary: We present a brief description and computer visualization of various scenarios of ideal turbulence, which is a kind of space-time chaos in idealized models of mathematical physics.

MSC:

76F20 Dynamical systems approach to turbulence
76M27 Visualization algorithms applied to problems in fluid mechanics
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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References:

[1] A. N. Sharkovsky and E. Yu. Romanenko, “Turbulence: ideal,” in: A. Scott (editor), Encyclopedia of Nonlinear Science, Routledge, New York (2005), pp. 955-957.
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[8] A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, and V. V. Fedorenko, Dynamics of One-Dimensional Maps [in Russian], Naukova Dumka, Kiev (1989); English translation: Kluwer Academic Publishers, Dordrecht (1997). · Zbl 0881.58020
[9] O. Yu. Romanenko, “Self-stochasticity phenomenon in dynamical systems generated by difference equations with continuous argument,” Ukr. Mat. Zh.,58, No. 7, 954-975 (2006); English translation: Ukr. Math. J.,58, No. 7, 1079-1105 (2006). · Zbl 1113.37036
[10] E. Yu. Romanenko, “Randomness in deterministic continuous time difference equations,” J. Difference Equat. Appl.,16, No. 2-3, 243-268 (2010). · Zbl 1193.37014
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