Global Attractors Of Non-linear Dynamic Systems

In this paper, we study the proving of the global attractors in different dynamic systems,and we give the direct proving of the equal conditions. The main results are the following:(1) We introduce something about the global attractors and give my main results.(2) In Chapter 2, we introduce two necessary and sufficient conditions for proving theexistence of the global attractors for semigroup, i.e. in autonomous systems, then we provethat the two conditions equal directly.(3) In Chapter 3, we introduce a necessary condition and a sufficient condition for the ex-istence of the global attractors in non-autonomous systems, then we consider what conditionwe need to prove the two conditions above are equal, and give the direct proving.(4) In Chapter 4, we change Definition 3.5 to that coincides withω-limit compact, thenwe can have a result similar to Theorem 2.4 without the nested condition. At last, we givethe similar definitions and parallel results in stochastic dynamical systems.