| 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) |
| Journal 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 keywords | Language |
|---|
| Operator matrix · Non-self-adjoint boundary eigenvalue problem · Keldysh chain · Multiple eigenvalue · Diabolical
point · Exceptional point · Perturbation · Bifurcation · Stability · Veering · Spectral mesh · Rotating continua | English |
|
| 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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