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Article

The Energy Function of Gradient-Like Flows and the Topological Classification Problem

Mathematical notes. 2014. Vol. 96. No. 6. P. 921-927.
Gurevich E., Grines V., Pochinka O.

For gradient-likeflows without heteroclinic intersections of the stable and unstable manifolds of saddle periodic points all of whose saddle equilibrium states have Morse index 1 or n−1, the notion of consistent equivalence of energy functions is introduced. It is shown that the consistent equivalence of energy functions is necessary and sufficient for topological equivalence.