On a class of locally reducible nonlinear systems of ordinary differential equations with perturbations in the form of homogeneous vector polynomials

The article received a extension of the class is locally reducible nonlinear systems of ordinary differential equations with perturbations in the form of homogeneous vector polynomials to linear systems with constant matrix. The method of proof is based on constructing a nonlinear Lyapunov transformation, linking the corresponding solutions of linear and nonlinear systems. The proof of the existence of a nonlinear Lyapunov transformation based on the application of the theorem on a fixed point operator, in particular the contraction mapping principle. Using the information in the article sufficient conditions of extendibility decisions right on the endless pollinterval and left on the final interval, as well as estimates for the norms of solutions of nonlinear systems, the author showed that the nonlinear operator based nonlinear Lyapunov transformation is an operator of compression. The article considers the example of a nonlinear differential equation, for which sufficient conditions for local reducibility are necessary.