Literature cited
M. I. Rabinovich, “Stochastic self-oscillations and turbulence,” Usp. Fiz. Nauk.,125, No. 1 (1978).
J.-P. Echmann, “Roads to turbulence in dissipative dynamical systems,” Rev. Mod. Phys.,53, 643 (1981).
J. Marsden and M. McCracken, Bifurcation of Creation of a Cycle and its Application [Russian translation], Mir, Moscow (1980).
V. I. Arnold, Supplementary Chapters of the Theory of Ordinary Differential Equations [Russian translation], Mir, Moscow. (1978).
R. D. Richtmyer, Principles of Modern Mathematical Physics [Russian translation], Mir, Moscow (1984).
J. Farmer, E. Ott, and J. Yorke, “The dimension of chaotic attractors,” Physica D,7, 153 (1983).
S. N. Lukashchuk, A. A. Predtechenskii, G. E. Fal'kovich, and A. I. Chernykh, “Calculation of the dimensions of attractors from experimental data,” [in Russian], Preprint Inst. Avtomat. Elektrom., Sib. Otd., SSSR, Novosibirsk, No. 280 (1985).
V. S. L'vov, A. A. Predtechenskii, and A. I. Chernykh, “Bifurcation and chaos in a system of Taylor vortices: a natural and numerical experiment,” Zh. Éksp. Teor. Fiz.,80, No. 3 (1981).
S. N. Lukashchuk and A. A. Predtechenskii, “Observation of resonance tori in the phase space of Couette flow,” Dokl. Akad. Nauk SSSR,274, No. 6 (1984).
N. Packard, J. Crutchfield, et al., “Geometry from a time series,” Phys. Rev. Lett.,45, No. 9 (1980).
F. Takens, “Detecting strange attractors in turbulence,” in: Lecture Notes in Mathematics,898, Springer-Verlag, Berlin (1980).
A. Brandstater, J. Swift, et al., “Low-dimensional chaos in a hydrodynamic system,” Phys. Rev. Lett.,51, No. 16 (1983).
A. Brandstater, J. Swift, H. Swinney, and A. Wolf, “A strange attractor in a Couette-Taylor experiment,” in: Turbulent and Chaotic Phenomena in Fluids: Proceedings IUTAM Symposium, Kyoto, 1983, North-Holland, Amsterdam (1984).
B. Malraison, P. Atten, et al., “Dimensions of strange attractors. An experimental determination: for the: chaotic regime of two convective systems,” J. Phys. Lett.,49, 897 (1983).
J. Roux, R. Simonyi, and H. Swinney, “Observation of the strange attractor,” Physica D,8, 257 (1983).
J. Guckenheimer and J. Buzyna, “Dimension measurements for geostrophic turbulence,” Phys. Rev. Lett.,51, 1438 (1983).
M. Giglio, S. Musazzi, and S. Umberto, “Low-dimensionality turbulent convection,” Phys. Rev. Lett.,53, 2402 (1984).
A. V. Gaponov-Grekhov, M. I. Rabinovich, and I. M. Starobinets, “Dynamic model of the spatial development of turbulence,” Pis'ma Zh. Eksp. Teor. Fiz.,39, No. 12 (1984).
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 99–104, January–February, 1989.
We thank V. S. L'vov and A. A. Predtechenskii for their discussion of the work and E. A. Kuznetsov for a stimulating influence during the writing.
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Lukashchuk, S.N., Fal'kovich, G.E. & Chernykh, A.I. Calculation of the dimensions of attractors from experimental data. J Appl Mech Tech Phys 30, 95–100 (1989). https://doi.org/10.1007/BF00860711
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DOI: https://doi.org/10.1007/BF00860711