The first Lyapunov method for stongly nonlinear systems of differential equations.

*(English)*Zbl 1040.34061Summary: The article is aimed to give a brief review on works published by the authors during at least last 10 years and devoted to the construction of solutions of systems of ordinary differential equations in a neighbourhood of a nonelementary critical point. It is assumed that those solutions have non-exponential asymptotics. The main idea of the proposed technique is closely connected with the so-called first Lyapunov method. On the first stage, one should cut the original system of equations in an appropriate way, then find a particular solution of the obtained cut system and, finally, complete it up to a particular solution of the entire system by means of series. The authors show how the above scenario works for different classes of dynamical objects.

##### MSC:

34D20 | Stability of solutions to ordinary differential equations |

70H14 | Stability problems for problems in Hamiltonian and Lagrangian mechanics |