Discussion Of Symplectic-Lie Group And Differential Dynamic Systems

In this paper,Lie group,Symplectic manifolds,Groupoids are treated as fundamental research subjects .Lie group has the special characteristics, that is,Lie group is not only a group but also a differential manifolds ,so the symplectic structure and the affine groups can be generalized on it.Finally,the representations of local coordinate on the differential dynamic systems of some fibre bundles are deduced.The whole paper is divided into four parts as below:1.Symplectic-Lie group ;2.Symplectic-Affine group and its characteristics;3.Discussions on the Groupoids;4.Differential dynamic systems of some fibre bundles.In the first section ,the Symplectic-Lie group is defined and many characteristics about it are investigated.In section 2 and section 3,the characteristics of the Symplectic-Affine group and diffeomorphism on the Groupoids are studied respectively.In section 4 ,the representations which are about local coordinate of the differential dynamic systems on principal bundle and tangent bundle are discussed.