Approximation of attractors for evolution equations with the help of attractors for finite systems

The problem of approximation of attractors for semidynamical systems (SDS) in a metric space is considered. Let some (exact) SDS possessing an attractor $M$ be inaccurately defined, i.e. another SDS, which is close in some sense to the exact one be given. The problem is to construct a set $\widetilde{M}$, which is close to $M$ in Hausdorff metric. A finite procedure for construction of $\widetilde{M}$ is suggested. The obtained results are suitable for numerical construction of attractors for rather large class of systems, including one generated by the Lorenz equations.