This article is cited in 5 papers

Normal form of differential equations with a small parameter

A. D. Bruno

Applied Mathematics Institute, Academy of Sciences of the USSR

Abstract: In this paper we study a system of ordinary differential equations with a small parameter in the neighborhood of a fixed solution. We find a normal form for such a system. Then for the case of a small parameter and a single resonance we show that the formal integral manifold, found by V. I. Arnol'd (see Referativnyi Zhurnal Matematika, 8B678), is not always analytic. We discuss the conditions under which it is analytic.

UDC: 517.9

Received: 18.12.1973

 English version: Mathematical Notes, 1974, 16:3, 832–836

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