Abstract
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.
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Original Russian Text © V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, 2014, published in Matematicheskie Zametki, 2014, Vol. 96, No. 6, pp. 856–863.
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Grines, V.Z., Gurevich, E.Y. & Pochinka, O.V. The energy function of gradient-like flows and the topological classification problem. Math Notes 96, 921–927 (2014). https://doi.org/10.1134/S0001434614110297
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DOI: https://doi.org/10.1134/S0001434614110297