Finite-dimensional oscillatory models in the general relativity theory and in gas dynamics

Methods of the qualitative theory of differential equations are applied to the homogeneous cosmological models and to a star explosion model in the classical dynamics of gases. Strongly degenerate singular points of these dynamical systems are studied using special coordinate transformations ($\sigma$-process). Trajectories are approximated by the sequences of separatrices for the non-degenerate singular points. Limit cycles are studied.