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Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices

Kirillov, O. N. (2009):
Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices.
61, In: Zeitschrift für Angewandte Mathematik und Physik (ZAMP), (2), Birkhäuser Verlag Basel/Switzerland, pp. 221-234, [Article]

Item Type: Article
Erschienen: 2009
Creators: Kirillov, O. N.
Title: Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices
Language: English
Journal or Publication Title: Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Volume: 61
Number: 2
Publisher: Birkhäuser Verlag Basel/Switzerland
Divisions: 16 Department of Mechanical Engineering > Dynamics and Vibrations
16 Department of Mechanical Engineering
Date Deposited: 19 Sep 2012 14:19
Identification Number: doi:10.1007/s00033-009-0032-0
Alternative keywords:
Alternative keywordsLanguage
Operator matrix · Non-self-adjoint boundary eigenvalue problem · Keldysh chain · Multiple eigenvalue · Diabolical point · Exceptional point · Perturbation · Bifurcation · Stability · Veering · Spectral mesh · Rotating continuaEnglish
Alternative Abstract:
Alternative abstract Language
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter λ and on the vector of real physical parameters p. We study perturbations of semi- simple multiple eigenvalues as well as perturbations of non-derogatory eigenvalues under small variations of p. Explicit formulae describing the bifurcation of the eigenvalues are derived. Application to the problem of excitation of unstable modes in rotating continua such as spherically symmetric MHD α2 -dynamo and circular string demonstrates the efficiency and applicability of the approach.English
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