On the convergence of dynamic quasi-periodic systems

The convergence problem for non-autonomous systems of differential equations with a quasi-periodic right-hand side in an independent argument is considered. It is proposed to replace the consideration of the set of solutions of the system of differential equations under consideration by considering the movements of a dynamic quasi-periodic system generated by these differential equations. Necessary and sufficient conditions are obtained when a dynamic quasi-periodic system has the convergence property, and a proof is given.