Compact Global Attractors

The second chapter is dedicated to the study of different types of dissipativity for dynamical systems (both autonomous and nonautonomous): point, compact, local, bounded, and the weak one. We give the criteria of a point, compact and local dissipativity. It is shown that for dynamical systems in locally compact spaces any three types of dissipativity are equivalent. Examples are given showing that in the general case the notions of point, compact, and local dissipativity are different. The notion of Levinson’s center (the compact global attractor), which is an important characteristic of compact dissipative system, is introduced.