Geodesic
IInvestigation of the sets of real solutions of non-linear equations
Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 199-213.

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We study the problem of constructing a smooth curve lying on the level set of a smooth map and issuing from an abnormal point. We find sufficient conditions for the existence of such curves and obtain bounds for the distances to level sets of the smooth map near an abnormal point.
Keywords: abnormal point, smooth curve, quadratic map, regular zero of a quadratic map, bound for the distance to a level set. 
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A. V. Arutyunov. IInvestigation of the sets of real solutions of non-linear equations. Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 199-213. http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a1/

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