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Matematicheskie Zametki, 2014, Volume 96, Issue 6, Pages 856–863
DOI: https://doi.org/10.4213/mzm10561 (Mi mzm10561) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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

V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka

N. I. Lobachevski State University of Nizhni Novgorod
Full-text PDF (566 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm10561
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.
Keywords: energy function, gradient-like flow, consistently equivalent energy functions, topological equivalence, Morse function, Morse index, self-indexing energy function.
Received: 22.01.2014
English version:
Mathematical Notes, 2014, Volume 96, Issue 6, Pages 921–927
DOI: https://doi.org/10.1134/S0001434614110297
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
Citation: V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “The Energy Function of Gradient-Like Flows and the Topological Classification Problem”, Mat. Zametki, 96:6 (2014), 856–863; Math. Notes, 96:6 (2014), 921–927
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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