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Finite-dimensional stochastic attractors of infinite-dimensional dynamical systems. (English. Russian original) Zbl 0619.58031
Funct. Anal. Appl. 20, 128-130 (1986); translation from Funkts. Anal. Prilozh. 20, No. 2, 54-55 (1986).
The author offers a special method for construction of infinite- dimensional dynamical systems from finite-dimensional dynamical systems. He shows that in this case the existence of a stochastic attractor for the finite-dimensional system leads to the existence of a finite- dimensional stochastic attractor for the corresponding infinite dimensional system.
Reviewer: Yu.E.Gliklikh
MSC:
37A99 Ergodic theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Ya. G. Sinai, in: Nonlinear Waves [in Russian], Nauka, Moscow (1979), pp. 192-212.
[2] M. V. Jacobson, Commun. Math. Phys.,81, No. 1, 39-88 (1981). · Zbl 0497.58017 · doi:10.1007/BF01941800
[3] A. V. Babin and M. I. Vishik, Usp. Mat. Nauk,38, No. 4, 133-187 (1983).
[4] E. B. Vul, Ya. G. Sinai, and K. M. Khanin, Usp. Mat. Nauk,39, No. 3, 3-37 (1984).
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