DIMENSION ESTIMATES FOR ATTRACTORS AND FOR KERNEL SECTIONS OF NONAUTONOMOUS EVOLUTION-EQUATIONS

In this Note we study non-autonomous evolution equations whose coeffic ients depend quasiperiodically on time. We present estimates from abov e and from below for the Hausdorff dimension of attractors of processe s generated by: 1) the two-dimensional Navier-Stokes system with a qua siperiodic external force, 2) the reaction-diffusion system with a qua siperiodic in time nonlinear interaction function and with a quasiperi odic external force, 3) the non-autonomous dissipative hyperbolic equa tion containing quasiperiodic terms. In the case when coefficients of these equations are general functions depending on time, we present es timates from above for the Hausdorff dimension of kernel sections of t hese equations. The kernel means the collection of all bounded solutio ns of the equation determined on the whole time axis.