Geodesic
Finite systems of equations and implicit functions.~I
Trudy Instituta matematiki, Tome 17 (2009) no. 2, pp. 3-14

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The well known Rückert–Lefschetz scheme of investigation of implicit functions that are defined with finite systems of equations with analytical left-hand sides. It is proved that this scheme is not effective. More exactly, this scheme does not allow to define jets of implicit functions using only jets of left-hand sides of equations under considerations even for structurally stable systems of equations. 
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P. P. Zabreiko; A. V. Krivko-Krasko. Finite systems of equations and implicit functions.~I. Trudy Instituta matematiki, Tome 17 (2009) no. 2, pp. 3-14. http://geodesic.mathdoc.fr/item/TIMB_2009_17_2_a0/