The Attractor Of Operator Semigroup On The Topological Vector Space

The(?)class operator semigroup is defined on the separation topological linear space,and theA(?)class and B-A(?)are defined in conjunction with the concept of the network in the topological linear space Class operator semi-groups.With the concept of distance in topological linear space,combined with topological knowledge,we use the network instead of the sequence and the set plus any zero neighborhood instead of any epsilon-neighborhood of the set,and the limit set is studied by the method of the double Cartesian orientation set defined by Mr.Xia Daoxing.The related concepts and conclusions of the attractor of the operator semigroups in the separation topological linear space play a key role.The properties of the ?-limit set of the three kinds of operator semigroup-s are studied in the separation of the topological linear spaces.The sufficient conditions for the existence of the minimal attractors of the corresponding oper-ator semigroups are given.The relation between the ?-the limit set of the cor-responding operator semigroup and the corresponding global attractor.Finally,we give the existence theorem of the minimal closed global B-attractor,and study the separation of topological linearity The relation between the minimal B-attractor and the ?-limit set is discussed,and the connectivity of the min-imal closed B-attractor is discussed.A O.Ladyzenskaya and Prof.Liu De,Inner Mongolia University The ?-limit set,the global attractor and the global B-attractor of these three kinds of operator semigroups in the metric space are generalized to the separate topological linear space.For example,(?)class operator semantics {Vt},A c X is defined on the separate topological linear space X and T? R+.If the orbital rT+(A)is bounded,then ?-(A)is a nonempty minimal compact set that attracts A and if A is con-nected and the semigroup ?(A)is also connected in the context of {Vt}.(?)class on the separate topological linear space or A(?)If there is Tx ? 0 for any x ? X,then the track rTx+(x)is bounded,then {Vt} has a nonempty minimal closed glob-al attractor(?)=[Ux?X?(x)lX,and for any t ? 0,Vr((?))(?)(?).In addition,for any closed F that contains Ux?X?(x),if the points are positive Poisson stable,then F =(?)And so on.