This article is cited in 1 paper

On the Pseudonormal Form of Real Autonomous Systems with Two Pure Imaginary Eigenvalues

V. S. Samovol

National Research University "Higher School of Economics"

Abstract: The paper deals with real autonomous systems of ordinary differential equations in a neighborhood of a nondegenerate singular point such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. The reducibility of such systems to pseudonormal form is studied. The notion of resonance is refined, and the notions of removable and irremovable resonances are introduced.

Keywords: ordinary differential equations, linearization, normal form, pseudonormal form, resonance.

UDC: 517.91

Received: 06.10.2011

DOI: 10.4213/mzm10039

 English version: Mathematical Notes, 2012, 92:5, 673–685

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