Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation

Kirillov, O. N.; Mailybaev, A. A.; Seyranian, A. P.

Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation

Authors

Kirillov, O. N.

Mailybaev, A. A.

Seyranian, A. P.

Description

The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical surface for different kinds of perturbing matrices are derived. As a physical application, singularities of the surfaces of refractive indices in crystal optics are studied.
23 pages, 7 figures