The problem of approximation of attractors for semidynamical systems (SDSs) in a metric space is studied. Let some (exact) SDS possessing an attractor M be inaccurately defined, i.e. let another (approximate) SDS, which is close in some sense to the exact one, be given. The problem is to construct a set , which is close to M in the Hausdorff metric.
The suggested procedure for constructing is finite, which makes it possible to use it in computations. The results obtained are suitable for numerical approximation of attractors for a rather large class of semidynamical systems, including ones generated by the Lorenz equations and the Navier–Stokes equations.