Geodesic
On limit sets of trajectories of dynamical systems of gradient type
Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 447-458 
M. V. Fokin. On limit sets of trajectories of dynamical systems of gradient type. Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 447-458. http://geodesic.mathdoc.fr/item/SM_1983_44_4_a2/
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     author = {M. V. Fokin},
     title = {On limit sets of trajectories of dynamical systems of gradient type},
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     year = {1983},
     volume = {44},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_4_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The structure of limit sets of the solutions of systems of differential equations having the form $\frac{dx}{dt}=-\nabla U(x)$, $x\in\mathbf R^n$, is studied. It is proved that any set of stationary points admissible for a general class of dynamical systems in $\mathbf R^n$, 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. Bibliography: 8 titles.

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[6] Zelenyak T. I., “O stabilizatsii reshenii kraevykh zadach dlya parabolicheskogo uravneniya vtorogo poryadka s prostranstvennoi peremennoi”, Diff. uravneniya, 4:1 (1968), 34–45 | Zbl

[7] Belonosov V. S, Zelenyak T. I., Nelokalnye problemy v teorii kvazilineinykh parabolicheskikh uravnenii, NGU, Novosibirsk, 1975 | MR

[8] Fokin M. V., “Suschestvovanie funktsionalov Lyapunova i stabilizatsiya reshenii dinamicheskikh i parabolicheskikh sistem pri $t \to \infty$”, Matematicheskie problemy khimii, ch. I, Novosibirsk, 1975, 120–123