Formal Asymptotics of Parametric Subresonance

The article is devoted to a comprehensive study of linear equations of the second order with an almost periodic coefficient. Using an asymptotic approach, the system of equations for parametric subresonant growth of the amplitude of oscillations is obtained. Moreover, the time of a turning point from the growth of the amplitude to the bounded oscillations in the slow variable is found. Also, a comparison between the asymptotic approximation for the turning time and the numerical one is shown.