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Realisation of an directed equipped bipartite graph by an Omega-stable flow on a closed surface

TitleRealisation of an directed equipped bipartite graph by an Omega-stable flow on a closed surface
AuthorsV. E. Kruglov1, 2, O. V. Pochinka1
1National Research University Higher School of Economics
2Lobachevsky State University
AnnotationA lot of many sorts of graphs (directed, multicolored, bipartite, etc.) were repeatedly used to describe and realize systems with regular dynamics on surfaces. For example, Morse-Smale flows are completely described by a directed graph equipped with a subgraph system. In addition, their dynamics can be described by three-color graphs. Four-color graphs describe the dynamics of some non structurally unstable vector fields, and a directed bipartite graph, equipped with additional information, is a complete topological invariant for $\Omega$-stable flows. In this paper, for each oriented equipped bipartite graph, we construct a standard $\Omega$-stable flow on a closed surface.
Keywordsrealisation, $\Omega$-stable flow, equipped graph
CitationKruglov V. E., Pochinka O. V. ''Realisation of an directed equipped bipartite graph by an Omega-stable flow on a closed surface'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 418-427. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper59.pdf. - Date of access: 11.12.2019.