The recognition problem for equivariant singularities
- 1 February 1988
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 1 (1) , 215-240
- https://doi.org/10.1088/0951-7715/1/1/009
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, (1985), the author shows for contact equivalence that in many cases the unipotent problem can be solved by just using linear algebra. He gives a necessary and sufficient condition for this, namely that the tangent space be invariant under unipotent equivalence. He then develops efficient methods for checking whether the tangent space is invariant, and gives several examples drawn from equivariant bifurcation theory.Keywords
This publication has 6 references indexed in Scilit:
- Classification of one-state-variable bifurcation problems up to codimension sevenDynamics and Stability of Systems, 1986
- Classification of Z(2)-Equivariant Imperfect Bifurcations with Corank 2Proceedings of the London Mathematical Society, 1983
- A discussion of symmetry and symmetry breakingPublished by American Mathematical Society (AMS) ,1983
- Imperfect bifurcation in the presence of symmetryCommunications in Mathematical Physics, 1979
- A theory for imperfect bifurcation via singularity theoryCommunications on Pure and Applied Mathematics, 1979
- Smooth functions invariant under the action of a compact lie groupTopology, 1975