zbMATH — the first resource for mathematics

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)

37D15 Morse-Smale systems
Full Text: DOI