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Finite-dimensional attractors in a turbulence model. (Russian) Zbl 0665.58025
Asymptotic properties of the infinite-dimensional system $\epsilon \dot x(t)=f(x(t-1))-x(t),\quad \epsilon \geq 0$ are studied in a general many-dimensional case that the mapping f is given in $$R^ d$$, $$d\geq 1$$. It is proved that for all $$\epsilon >0$$ this system has a finite- dimensional attractor. Estimates of its dimension are obtained as function of the parameter $$\epsilon$$.
Reviewer: J.H.Tian

##### MSC:
 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
##### Keywords:
finite-dimensional attractors; turbulence model