Geodesic
On limit sets of trajectories of dynamical systems of gradient type
Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 447-458

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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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     author = {M. V. Fokin},
     title = {On limit sets of trajectories of dynamical systems of gradient type},
     journal = {Sbornik. Mathematics},
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     volume = {44},
     number = {4},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_4_a2/}
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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/