THE STRUCTURE OF THE SINGULAR SYMPLECTIC MATRIX SET
Yi Ming Long · 1991
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.