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Circular Fleitas Scheme for Gradient-Like Flows on the Surface
Vladislav D. Galkin, Elena V. Nozdrinova, Olga V. Pochinka HSE University,
ul. Bolshaya Pecherckaya 25/12, 603155 Nizhny Novgorod, Russia
Abstract:
In this paper, we obtain a classification of gradient-like flows on arbitrary surfaces
by generalizing the circular Fleitas scheme. In 1975 he proved that such a scheme is a complete
invariant of topological equivalence for polar flows on 2- and 3-manifolds. In this paper, we
generalize the concept of a circular scheme to arbitrary gradient-like flows on surfaces.We prove
that the isomorphism class of such schemes is a complete invariant of topological equivalence.
We also solve exhaustively the realization problem by describing an abstract circular scheme
and the process of realizing a gradient-like flow on the surface. In addition, we construct an
efficient algorithm for distinguishing the isomorphism of circular schemes.
Keywords:
gradient-like flows, circular scheme, flows on the surface.
Received: 03.02.2023 Accepted: 25.10.2023
Citation:
Vladislav D. Galkin, Elena V. Nozdrinova, Olga V. Pochinka, “Circular Fleitas Scheme for Gradient-Like Flows on the Surface”, Regul. Chaotic Dyn., 28:6 (2023), 865–877
Linking options:
https://www.mathnet.ru/eng/rcd1238 https://www.mathnet.ru/eng/rcd/v28/i6/p865
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Abstract page: | 39 | References: | 12 |
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