On periodic solutions of the four-dimensional differential system of Lyapunov-Darboux type with quadratic nonlinearities

Abstract

For the four-dimensional differential system of LyapunovDarboux type with quadratic nonlinearities, we have found a holomorphic integral of Lyapunov type. Using this integral and the Lyapunov theorem, we have obtained centro-affine invariant conditions for stability of unperturbed periodic motion.