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Regular version of the site

Article

Pseudonormal Form and FiniteSmooth Equivalence of Real Autonomous Systems with Two Purely Imaginary Eigenvalues

Доклады Академии наук. 2012. Vol. 85. No. 1. P. 122-124.

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.