Bifurcation points of rotating magnetized Newtonian polytropes with an index close to unity

The existence of bifurcation points of Newtonian rotating polytropes in the interval of polytropic index 0.9989 < n ≤ 1.0795, in which asymmetric with respect to the axis of rotation solutions describing the density distribution are branched, is proved for the first time. It is shown that, in this interval of values of n, the parameter of the rotation rate at critical points ε_k takes values 0.0442 > ε_k ≥ 0.