This article is cited in 2 papers

Finite systems of equations and implicit functions. I

P. P. Zabreiko^a, A. V. Krivko-Krasko<sup>b

a</sup> Institute of Mathematics of the National Academy of Sciences of Belarus
^b Belarusian State University

Abstract: 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.

UDC: 517.948:330.105

Received: 17.06.2009