# Poénaru (1976) theorem

Let $\Gamma$ be a compact Lie group and let $g_{1},\ldots,g_{r}$ generate the module $\vec{\mathcal{P}}(\Gamma)$(the space of $\Gamma$-equivariant polynomial mappings) of $\Gamma$-equivariant polynomials over the ring $\mathcal{P}(\Gamma)$(the ring of $\Gamma$-invariant polynomial). Then $g_{1},\ldots,g_{r}$ generate the module $\vec{\mathcal{E}}(\Gamma)$(the space of $\Gamma$-equivariant germs at the origin of $C^{\infty}$ mappings) over the ring $\mathcal{E}(\Gamma)$(the ring of $\Gamma$-invariant germs). [GSS]

## References

• GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
• PV Poénaru, V.:Singularités $C^{\infty}$ en Présence de Symétrie. Lecture Notes in Mathematics 510, Springer-Verlag, Berlin, 1976.
Title Poénaru (1976) theorem Poenaru1976Theorem 2013-03-22 13:40:59 2013-03-22 13:40:59 mathcam (2727) mathcam (2727) 6 mathcam (2727) Theorem msc 37G40