The Cone and Squeezing Properties. Inertial Manifolds

Our aim in this final chapter is to introduce the concept of inertial manifolds for dissipative dynamical systems. This is a new concept which has recently emerged in nonlinear dynamics and, here, we shall restrict ourselves to describing a few typical results. Our presentation follows with some slight simplifications and generalizations C. Foias, G. Sell, and R. Temam [1], [2], C. Foias, B. Nicolaenko, G. Sell, and R. Temam [1], [2]. The reader is referred to Remark 4.3 for some bibliographical references on this rapidly expanding subject.