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## О топологии многообразий, допускающих градиентно-подобные потоки с заданным неблуждающим множеством

Математические труды. 2018. Т. 21. № 2. С. 163-180.

In this paper, we study the relationship between the structure of the set of equilibrium states of a gradient-like flow and the topology of a carrier manifold of dimension 4 and higher. We introduce a class of manifolds admitting a generalized Heegaard decomposition. It is established that if a non-wandering set of a gradient-like flow consists of exactly $\ mu$ nodal and $\ nu$ saddle equilibrium states of the Morse indices $1$ and $(n-1)$, then its carrying manifold admits a generalized Heegaard decomposition of genus $g = \ frac {\ nu- \ mu 2} {2}$. An algorithm is given for constructing gradient-like flows on closed manifolds of dimension $n \ geq 3$ with respect to a given number of nodal equilibrium states and given numbers of saddle equilibrium states for various Morse indices.