13A50-InvariantPolynomial.tex

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\pmtitle{invariant polynomial}
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An \emph{invariant polynomial} is a polynomial $P$ that is invariant under a \text{(compact)} Lie group $\Gamma$ acting on a vector space $V$.  Therefore $P$ is $\Gamma$-invariant polynomial if $P(\gamma x) = P(x)$ for all $\gamma \in \Gamma$ and $x \in V$.
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\bibitem[GSS]{1} Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory \textit{(Volume II)}. Springer-Verlag, New York, 1988.
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