On the bifurcation set of a polynomial function and Newton boundary, II

Let /: C-*C be a polynomial function. It is well known that there exists a finite set TgC, such that /: C\f-(F^C\r is a locally trivial fibration (see [1], [5], [13], [15], [16]). The smallest such set F we call the bifurcation set, denoted by Bf (in [1], [2] it is called the set of atypical values). Since the map / is not proper, the set Bf contains besides the set J^/ of all critical values of / perhaps some other points (the "critical values at infinity" or "critical values of second type" [12]). There are some special cases when the polynomial has no critical values at infinity (hence Bf=If):Pham [13] and Fedoryuk [4] have imposed lowerbound conditions for ||grad/(x)|| f° large values of \\x\\, Kouchnirenko has proved in [6] for convenient polynomials with nondegenerate Newton principal part at infinity, Broughton [1], [2] for "tame" polynomials and the first author [8], [9] for the larger class of "quasitame" polynomials. In this note we give an explicit set Sf, such that Bf^Sf\JSf. More