  In this paper, we determine the bifurcation set of a real polynomial function
of two variables for non-degenerate case in the sense of Newton polygons by
using a toric compactification. We also count the number of singular phenomena
at infinity, called "cleaving" and "vanishing" in the same setting. Finally, we
give an upper bound of the number of elements in the bifurcation set in terms
of its Newton polygon. To obtain the upper bound, we apply toric modifications
to the singularities at infinity successively.

Geometric Topology;Algebraic Geometry