Generic Movement of Eigenvalues for Equivariant Selfadjoint Matrices

J. Comp. Appl. Math. 55 (1994) 249-259

Michael Dellnitz and Ian Melbourne


In the numerical treatment of bifurcation problems one of the main tasks is to control the spectrum of matrices in a parametrized family. If the original problem possesses symmetry, then the matrices are additionally equivariant. Previously the generic eigenvalue behavior in a one-parameter family of equivariant matrices has been studied for the case of general matrices by Golubitsky, Stewart and Schaeffer and for infinitesimally symplectic matrices Dellnitz, Melbourne and Marsden. However, in applications the situation frequently occurs that the matrices of the family are selfadjoint. We classify the generic eigenvalue behavior in such a family of equivariant matrices by the type of underlying symmetry.