Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation
O. N. Kirillov, A. A. Mailybaev, A. P. Seyranian
Abstract
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.
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