Title | Realisation of an directed equipped bipartite graph by an Omega-stable flow on a closed surface |
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Authors | V. E. Kruglov^{1, 2}, O. V. Pochinka^{1}^{1}National Research University Higher School of Economics ^{2}Lobachevsky State
University |

Annotation | A 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. |

Keywords | realisation, $\Omega$-stable flow, equipped graph |

Citation | Kruglov 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: 12.04.2021. |

**© SVMO, National Research Mordovia State University, 2021**

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