Melbourne, Ian. (1988) The recognition problem for equivariant singularities. NONLINEARITY, 1 (1). pp. 215-240. ISSN 0951-7715

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Abstract

Singularity theory involves the classification of singularities up to some equivalence relation. The solution to a particular recognition problem is the characterisation of an equivalence class in terms of a finite number of polynomial equalities and inequalities to be satisfied by the Taylor coefficients of a singularity. The recognition problem can be simplified by decomposing the group of equivalences into a unipotent group and a group of matrices. Building upon results of Bruce and co-workers, we show for contact equivalence that in many cases the unipotent problem can be solved by just using linear algebra. We give a necessary and sufficient condition for this, namely that the tangent space be invariant under unipotent equivalence. We then develop efficient methods for checking whether the tangent space is invariant, and give several examples drawn from equivariant bifurcation theory.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	NONLINEARITY
Publisher:	IOP PUBLISHING LTD
ISSN:	0951-7715
Date:	February 1988
Volume:	1
Number:	1
Number of Pages:	26
Page Range:	pp. 215-240
Publication Status:	Published
Funder:	SERC
URI:	http://wrap.warwick.ac.uk/id/eprint/24618

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