Approximation of Attractors and Inertial Manifolds. Convergent Families of Approximate Inertial Manifolds

Our aim in this chapter is to study the approximation of attractors and inertial manifolds by smooth finite-dimensional manifolds, called approximate inertial manifolds. There is a vast and growing literature on approximation of attractors and inertial manifolds, approximate dynamics, and related algorithms. These important topics could justify, by themselves, the writing of one or several books; we will not try to give an exhaustive presentation or even an exhaustive bibliography on this question (see, however, a few references in Remark 3.2 at the end of this chapter).