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

In this Note we study non-autonomous evolution equations whose coefficients depend quasiperiodically on time. We present estimates from above and from below for the Hausdorff dimension of attractors of processes generated by: 1) the two-dimensional Navier-Stokes system with a quasiperiodic external force, 2) the reaction-diffusion system with a quasiperiodic in time nonlinear interaction function and with a quasiperiodic external force, 3) the non-autonomous dissipative hyperbolic equation containing quasiperiodic terms. In the case when coefficients of these equations are general functions depending on time, we present estimates from above for the Hausdorff dimension of kernel sections of these equations. The kernel means the collection of all bounded solutions of the equation determined on the whole time axis.