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The first Lyapunov method for stongly nonlinear systems of differential equations. (English) Zbl 1040.34061
Summary: 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.
34D20 Stability of solutions to ordinary differential equations
70H14 Stability problems for problems in Hamiltonian and Lagrangian mechanics