SET CONVERGENCE FOR DISCRETIZATIONS OF THE ATTRACTOR

We consider the discretization of a dynamical system given by a C-o-se migroup S(t), defined on a Banach space X, possessing an attractor d. Under certain weak assumptions, Hale, Lin and Raugel showed that discr etizations of S(t) possess local attractors, which may be considered a s approximations to A. Without further assumptions, we show that these local attractors possess convergent subsequences in the Hausdorff or set metric, whose limit is a compact invariant subset of A. Using a ne w construction, we also consider the Kloeden and Lorenz concept of att racting sets in a Banach space, and show under mild assumptions that d iscretizations possess attracting sets converging to A in the Hausdorf f metric.