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Milnor fibrations were extended by Mutsuo Oka for certain mixed polynomial.In this paper, we study singular points of differentiable maps into the2-dimensional torus, called Milnor fibration product maps, obtained by severalMilnor fibrations for mixed polynomial. We give a characterization of singularpoints of such product maps, and for the case of certain polar weightedhomogeneous polynomials, a criterion for a fold singular point.

Fold singularities of the maps associated with Milnor fibration for mixed polynomials