On eigenvalue surfaces near a diabolic point

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

doi:10.1109/PHYCON.2005.1514000

On eigenvalue surfaces near a diabolic point

O. N. Kirillov^*, Alexei Mailybaev, A. P. Seyranian

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The paper presents a 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.

Original language	English
Title of host publication	2005 International Conference on Physics and Control, PhysCon 2005, Proceedings
Editors	A L Fradkov
Place of Publication	St Petersburg
Pages	319-325
Number of pages	7
Volume	2005
DOIs	https://doi.org/10.1109/PHYCON.2005.1514000
Publication status	Published - 2005
Externally published	Yes
Event	2005 International Conference on Physics and Control, PhysCon 2005 - St. Petersburg, Russian Federation Duration: 24 Aug 2005 → 26 Aug 2005

Conference

Conference	2005 International Conference on Physics and Control, PhysCon 2005
Country/Territory	Russian Federation
City	St. Petersburg
Period	24/08/05 → 26/08/05

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10.1109/PHYCON.2005.1514000

Cite this

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title = "On eigenvalue surfaces near a diabolic point",

abstract = "The paper presents a 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.",

author = "Kirillov, {O. N.} and Alexei Mailybaev and Seyranian, {A. P.}",

year = "2005",

doi = "10.1109/PHYCON.2005.1514000",

language = "English",

isbn = "9780780392342",

volume = "2005",

pages = "319--325",

editor = "Fradkov, {A L}",

booktitle = "2005 International Conference on Physics and Control, PhysCon 2005, Proceedings",

note = "2005 International Conference on Physics and Control, PhysCon 2005 ; Conference date: 24-08-2005 Through 26-08-2005",

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Kirillov, ON, Mailybaev, A & Seyranian, AP 2005, On eigenvalue surfaces near a diabolic point. in AL Fradkov (ed.), 2005 International Conference on Physics and Control, PhysCon 2005, Proceedings. vol. 2005, 1514000, St Petersburg, pp. 319-325, 2005 International Conference on Physics and Control, PhysCon 2005, St. Petersburg, Russian Federation, 24/08/05. https://doi.org/10.1109/PHYCON.2005.1514000

TY - GEN

T1 - On eigenvalue surfaces near a diabolic point

AU - Kirillov, O. N.

AU - Mailybaev, Alexei

AU - Seyranian, A. P.

PY - 2005

Y1 - 2005

N2 - The paper presents a 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.

AB - The paper presents a 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.

UR - http://www.scopus.com/inward/record.url?scp=33746765156&partnerID=8YFLogxK

U2 - 10.1109/PHYCON.2005.1514000

DO - 10.1109/PHYCON.2005.1514000

M3 - Conference contribution

AN - SCOPUS:33746765156

SN - 9780780392342

VL - 2005

SP - 319

EP - 325

BT - 2005 International Conference on Physics and Control, PhysCon 2005, Proceedings

A2 - Fradkov, A L

CY - St Petersburg

T2 - 2005 International Conference on Physics and Control, PhysCon 2005

Y2 - 24 August 2005 through 26 August 2005

ER -

On eigenvalue surfaces near a diabolic point

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