Abstract
In this paper, we try to obtain a better understanding of geometrical meaning of Lyapunov's second method from the topological viewpoint and shall give an affirmative con- clusion of the existence and concrete construction of the family of surfaces,i.e. the generalized Lyapunov's function. Since the topological character of integral curves of differential equation is a regular curve, the existence problem of the family of closed surfaces, or the family of closed curves in plane, can be solved completely by means of the topological viewpoint, if the undisturbed move- ment is asymptotically stable in a generalized way.
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