Аннотация:
It is well known that the topological classification of structurally stable flows on surfaces as well as the topological classification of some multidimensional gradient-like systems can be reduced to a combinatorial problem of distinguishing graphs up to isomorphism. The isomorphism problem of general graphs obviously can be solved by a standard enumeration algorithm. However, an efficient algorithm (i. e., polynomial in the number of vertices) has not yet been developed for it, and the problem has not been proved to be intractable (i. e., NPcomplete). We give polynomial-time algorithms for recognition of the corresponding graphs for two gradient-like systems. Moreover, we present efficient algorithms for determining the orientability and the genus of the ambient surface. This result, in particular, sheds light on the classification of configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field.
This work was supported by the Russian Foundation for Basic Research (grants 15-01-03687-a, 16-31-60008-mol_a_dk), Russian Science Foundation (grant 14-11-00044), the Basic Research Program at the HSE (project 98) in 2016, by LATNA laboratory, National Research University Higher School of Economics, and by RF President grant MK-4819.2016.
Поступила в редакцию: 08.12.2015 Принята в печать: 04.02.2016
Образец цитирования:
Vyacheslav Z. Grines, Dmitry S. Malyshev, Olga V. Pochinka, Svetlana Kh. Zinina, “Efficient Algorithms for the Recognition of Topologically Conjugate Gradient-like Diffeomorhisms”, Regul. Chaotic Dyn., 21:2 (2016), 189–203
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\paper Efficient Algorithms for the Recognition of Topologically Conjugate Gradient-like Diffeomorhisms
\jour Regul. Chaotic Dyn.
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd74
https://www.mathnet.ru/rus/rcd/v21/i2/p189
Эта публикация цитируется в следующих 7 статьяx:
D. A. Baranov, O. V. Pochinka, D. D. Shubin, E. I. Yakovlev, “On Suspensions Over Gradient-Like Diffeomorphisms of Surfaces with Three Periodic Orbits”, J Math Sci, 284:1 (2024), 4
Е. Я. Гуревич, Е. К. Родионова, “Двухцветный граф каскадов Морса-Смейла на трехмерных многообразиях”, Журнал СВМО, 25:2 (2023), 37–52
В. З. Гринес, Е. Я. Гуревич, Е. В. Жужома, О. В. Починка, “Классификация систем Морса–Смейла и топологическая структура несущих многообразий”, УМН, 74:1(445) (2019), 41–116; V. Z. Grines, E. Ya. Gurevich, E. V. Zhuzhoma, O. V. Pochinka, “Classification of Morse–Smale systems and topological structure of the underlying manifolds”, Russian Math. Surveys, 74:1 (2019), 37–110
V. Z. Grines, Ye. V. Zhuzhoma, O. V. Pochinka, “Morse–Smale Systems and Topological Structure of Carrier Manifolds”, J Math Sci, 239:5 (2019), 549
Олена В'ячеславівна Ноздрінова, Ольга Віталіïвна Починка, “A calculation of periodic data of surface diffeomorphisms with one saddle orbit.”, PIGC, 11:2 (2018)
В. З. Гринес, Е. В. Жужома, О. В. Починка, “Системы Морса–Смейла и топологическая структура несущих многообразий”, Труды Крымской осенней математической школы-симпозиума, СМФН, 61, РУДН, М., 2016, 5–40
В. Е. Круглов, Д. С. Малышев, О. В. Починка, “Графовый критерий топологической эквивалентности Ω-устойчивых потоков без периодических траекторий на поверхностях и эффективный алгоритм для его применения”, Журнал СВМО, 18:2 (2016), 47–58
Цитирование в формате AMSBIB
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