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Singularities of dispersion relations

Published online by Cambridge University Press:  14 November 2011

G. Dangelmayr
G. Dangelmayr
Affiliation:
Institute for Information Sciences, University of Tübingen, Tübingen, Federal Republic of Germany
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Synopsis

Generic singularities occurring in dispersion relations are discussed within the framework of imperfect bifurcation theory and classified up to codimension four. Wave numbers are considered as bifurcation variables x =(x1,…, xn) and the frequency is regarded as a distinguished bifurcation parameter λ. The list of normal forms contains, as special cases, germs of the form ±λ +f(x), where f is a standard singularity in the sense of catastrophe theory. Since many dispersion relations are ℤ(2)-equivariant with respect to the frequency, bifurcation equations which are ℤ(2)-equivariant with respect to the bifurcation parameter are introduced and classified up to codimension four in order to describe generic singularities which occur at zero frequency. Physical implications of the theory are outlined.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 3-4 , 1983 , pp. 301 - 316
Copyright
Copyright © Royal Society of Edinburgh 1983

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