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Acta Mathematica Vietnamica

AN ESTIMATION OF THE NUMBER OF BIFURCATION VALUES FOR REAL POLYNOMIALS

HÀ HUY VUI, PHẠM TIẾN SƠN

Abstract

Let f:RnR 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 (d1)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.