摘要
<正> A symplectic matrix M is singular, if det(M-I)=0. In this paper we study the struc-ture of the singular set of symplectic mtrices. We discuss the changes of the dimension ofthe null space and the determinant of the difference between a singular symplectic matrixand the identity matrix under rotational perturbations. The results obtained will be used todefine a Maslov-type index theory for (degenerate) paths in symplectic groups, and thereforeto establish the existence of periodic solutions of asymptotically linear Hamiltonian systems.
A symplectic matrix M is singular, if det(M-I)=0. In this paper we study the struc-ture of the singular set of symplectic mtrices. We discuss the changes of the dimension ofthe null space and the determinant of the difference between a singular symplectic matrixand the identity matrix under rotational perturbations. The results obtained will be used todefine a Maslov-type index theory for (degenerate) paths in symplectic groups, and thereforeto establish the existence of periodic solutions of asymptotically linear Hamiltonian systems.
基金
Project supported by the National Natural Science Foundation of China.
