Stability and bifurcations in averaged models of dynamics

Averaging over fast phases reduces study of stability of quasi-periodic and periodic trajectories to study of stability of periodic trajectories and equilibria. The aim of the proposed research is to study stability properties in several averaged models of dynamics. Bifurcation analysis is the central tool in study of such properties. The first and second models that we study are the simple and the spherical pendulums {with vibrating suspension points}. We give a complete description of bifurcations of their phase portraits. Main part of the research is devoted to the restricted elliptic three body problem (ER3BP). This model with large eccentricities of the planet is of particular interest in relation to study of motion of exoplanets.