Abstract:
The structure of limit sets of the solutions of systems of differential equations having the form dxdt=−∇U(x), x∈Rn, is studied. It is proved that any set of stationary points admissible for a general class of dynamical systems in Rn, can be such a limit set. Sufficient conditions for the stabilization of the solutions to a stationary one are obtained for systems close to systems of gradient type.
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\Bibitem{Fok81}
\by M.~V.~Fokin
\paper On limit sets of trajectories of dynamical systems of gradient type
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 4
\pages 447--458
\mathnet{http://mi.mathnet.ru/eng/sm2479}
\crossref{https://doi.org/10.1070/SM1983v044n04ABEH000977}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=665851}
\zmath{https://zbmath.org/?q=an:0555.34022|0498.34020}
Linking options:
https://www.mathnet.ru/eng/sm2479
https://doi.org/10.1070/SM1983v044n04ABEH000977
https://www.mathnet.ru/eng/sm/v158/i4/p502
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