On the stability of the trivial solution to a periodic system of ordinary differential equations

In this paper, we examine a normal system of ordinary differential equations whose right-hand side is periodic in the independent variable and locally smoothly depends on the small parameter and the phase variable. Using the properties of nonlinear approximations of the right and left monodromy operators, we prove conditions that guarantee the arbitrary smallness of perturbed solutions for sufficiently small initial values of the solutions and the parameter.