Geodesic
The Energy Function of Gradient-Like Flows and the Topological Classification Problem
Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 856-863

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For gradient-like flows 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.
Keywords: energy function, gradient-like flow, consistently equivalent energy functions, topological equivalence, Morse function, Morse index, self-indexing energy function. 
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     author = {V. Z. Grines and E. Ya. Gurevich and O. V. Pochinka},
     title = {The {Energy} {Function} of {Gradient-Like} {Flows} and the {Topological} {Classification} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
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V. Z. Grines; E. Ya. Gurevich; O. V. Pochinka. The Energy Function of Gradient-Like Flows and the Topological Classification Problem. Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 856-863. http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a4/