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Article

О вложении инвариантных многообразий простейших потоков Морса-Смейла с гетероклиническими пересечениями

Гуревич Е. Я., Павлова Д. А.

We study a structure of four-dimensional phase space   decomposition on trajectories of  Morse-Smale flows admitting heteroclinical intersections.  We consider a class $G(S^4)$ of Morse-Smale flows on the sphere  $S^4$ such that for any flow  $f\in G(S^4)$ its non-wandering set consists of exactly four equilibria: source, sink and two saddles. Wandering set of such flows contains finite number of heteroclinical curves generating  the intersection of invariant manifolds of saddle equilibria.  We describe a topology of embedding of invariant manifolds of saddle equilibria  that is the first step in a solution of topological classification problem.