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Regular version of the site

Article

Polynomial normal form and finitely smooth equivalence of autonomous systems with one zero eigenvalue

Доклады Академии наук. 2010. Vol. 81. No. 3. P. 351-353.

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations for which one eigenvalue of the matrix of the linear part is zero and the remaining eigenvalues do not belong to the imaginary axis. We study the reducibility of such systems to normal 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.