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Topological aspects of dynamical systems. (Russian) Zbl 0755.58032
Nothing is proved in this paper. A number of results is established for minimal vector fields on a smooth closed manifold. Here, a minimal flow is defined to be a minimal element with respect to some partial order $$<$$ on the set of all vector fields on $$M$$ having finitely many critical points and periodic orbits, all of them hyperbolic. The order $$<$$ is defined by: $$X < Y$$ iff $$P_ i(X)\leq P_ i(Y)$$ and $$O_ i(X) \leq O_ i(Y)$$, for all $$i = 0,\dots,\dim M$$, where $$P_ i$$, resp. $$O_ i$$, denote the number of critical points, resp. periodic orbits, of index $$i$$ of vector fields $$X$$ and $$Y$$.
Reviewer: J.Ombach (Kraków)

##### MSC:
 37D15 Morse-Smale systems
##### Keywords:
Morse-Smale systems; Lyapunov function
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