Estimates of the fractal dimension and of the number of deterministic modes for invariant sets of dynamical sytsems

Majorants of the fractal dimension and of the number of determining modes for unbounded sets, invariant with respect to operators of semigroups of classes 1 and 2, are obtained. They are computed for the Navier–Stokes equations (two- and three-dimensional) under the first boundary condition and under periodicity conditions in the spaces $H^0\subset\vec L_2(\Omega)$ and $H^1\subset\vec W_2^1(\Omega)$ .