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Classification of symmetric caustics. I: Symplectic equivalence. (English) Zbl 0747.58015

Singularity theory and its applications. Pt. II: Singularities, bifurcations and dynamics, Proc. Symp., Warwick/UK 1988-89, Lect. Notes Math. 1463, 193-219 (1991).
[For the entire collection see Zbl 0723.00029.]
The authors generalize the classification theory of Arnol’d and Zakalyukin for singularities of Lagrange projections to projections that commute with a symplectic action of a compact Lie group up to symplectic equivalence. The theory is applied to the classification of infinitesimally stable corank 1 projections with \(Z_ 2\) symmetry.
Their approach to symplectic equivalence is a generalization of the non- equivariant theory of Arnol’d and Zakalyukin in that they use a form of parametrized right equivalence of Morse functions.
Reviewer: M.Adachi (Kyoto)

MSC:

58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
58E09 Group-invariant bifurcation theory in infinite-dimensional spaces

Citations:

Zbl 0723.00029
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