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In this article, we obtain, through statistical and numerical methods, asmooth function in the variables of the life stage and the concentration, whichestimates the risk of exposure of methylmercury due to the unintentionalconsumption of shark in men from Mexico City. With methods of the Theory ofSingularities and Dynamical Systems, the stability of this risk function wasshown by analyzing the associated vector field. The region of risk was obtainedin the variables as mentioned above, and the average risk in the whole regionwas calculated, which turns out to be a high index. The associated risk surfaceis a Hadamard surface embedded in the three-dimensional space $\mathbb{R}^3$,and the points where the curvature is zero determine critical ages importantfor the risk in men.

On a smooth scalar field characterizing the risk of exposure to  methyl-mercury due to non intentional consumption of shark meet in males of  M\'exico city's metropolitan area