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
[1]
Masakazu Suzuki.
Propri\'et\'es topologiques des polyn\^omes de deux variables complexes, et automorphismes alg\'ebriques de l'espace $C^{2}$
,
1974
.
[2]
Mutsuo Oka,et al.
On the bifurcation of the multiplicity and topology of the Newton boundary
,
1979
.
[3]
Jean-Louis Verdier,et al.
Stratifications de Whitney et théorème de Bertini-Sard
,
1976
.
[4]
A. G. Kouchnirenko.
Polyèdres de Newton et nombres de Milnor
,
1976
.
[5]
A N Varčenko,et al.
THEOREMS ON THE TOPOLOGICAL EQUISINGULARITY OF FAMILIES OF ALGEBRAIC VARIETIES AND FAMILIES OF POLYNOMIAL MAPPINGS
,
1972
.
[6]
S. Broughton.
On the Topology of Polynomial Hypersurfaces
,
1983
.
[7]
Sean A Broughton,et al.
Milnor numbers and the topology of polynomial hypersurfaces
,
1988
.