On the stability of unstable states, bifurcations, chaos at nonlinear dynamical systems.

The question of the stability of unstable states of dynamical systems that do not explicitly contain a small parameter, chaos and bifurcations in them has attracted attention ever since This is due to the fact that this problem often arises not only in mathematics, but also in various fields of mechanics and physics. In particular, the task of retaining atomic particles in electrodynamic traps has recently become of special interest.