Acta Mathematica Vietnamica

Let $f : \mathbb R^n \to \mathbb R$ be a polynomial of degree $d$ with only isolated complex critical points. It is shown that the set of bifurcation values of $f$ is contained in a set which has at most $(d −1)^n$ points. The proof of this result is done in such a way that all points of the last set can be explicitly calculated. As a consequence, we obtain a finite set containing the global infimum value of a bounded below polynomial.

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