Gunther Reißig and Holger Boche.

A Normal Form for Implicit Differential Equations Near Singular Points.

Proc. 1997 Europ. Conf. on Circuit Th. and Design (ECCTD), Budapest, Hu., Aug. 30-Sept. 3, 1997, vol. 2, 1048-1053.

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**Abstract:**

We consider differential equations A(x)x'=g(x), where A is a (n x n)-matrix of
C^{1}-functions and g is C^{1}.
We investigate the above differential equation about singular points x_{0} that are *standard*
in the sense of Rabier.
In particular, the null space of A(x_{0}) is of dimension 1.
We show that there is a C^{1}-diffeomorphism
that transforms the above equation about x_{0} into

x_{1} x_{1}' = +/-1,

x_{2}' = ... = x_{n}' = 0

about 0.

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