This article is cited in 4 papers

Normal form of real differential equations

A. D. Bruno

Applied Mathematics Institute, Academy of Sciences of the USSR

Abstract: In a neighborhood of a fixed point we consider an autonomous analytic system of ordinary differential equations. We establish the existence of a normalizing transformation for which the normal form retains the properties of the original system such as reality and invariance with respect to a linear change of variables. For real systems we consider the problem of existence of an analytic transformation into normal form and the problem of existence of a finitely smooth transformation into a linear system.

UDC: 517.9

Received: 01.11.1974

 English version: Mathematical Notes, 1975, 18:2, 722–731

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