Local finitely smooth equivalence of real autonomous systems with two pure imaginary eigenvalues

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. It is proved that, for such systems having a focus on the center manifold, the problem of finitely smooth equivalence is solved in terms of the finite segments of the Taylor series of their right-hand sides.