Geodesic
On real solutions of systems of equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 79-83.

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Systems of equations $f_1=\cdots=f_{n-1}=0$ в $\mathbb R^n=\{x\}$ in $\mathbb R^n=\{x\}$ having the solution $x=0$ are considered under the assumption that the quasi-homogeneous truncations of the smooth functions $f_1=\cdots=f_{n-1}$ are independent at $x\ne0$. It is shown that, for $n\ne2$ and $n\ne4$, such a system has a smooth solution which passes through $x=0$ and has nonzero Maclaurin series.
Keywords: quasi-homogeneous truncation, asymptotic solution. 
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V. V. Kozlov. On real solutions of systems of equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 79-83. http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a7/

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