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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.
MSC:
34D20 Stability of solutions to ordinary differential equations
70H14 Stability problems for problems in Hamiltonian and Lagrangian mechanics
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