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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
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