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- Title
Topological Conjugacy of Gradient-Like Flows on Surfaces and Efficient Algorithms for its Distinction.
- Authors
Kruglov, V. E.; Pochinka, O. V.
- Abstract
Gradient-like flows on surfaces have simple dynamics, which inspired many mathematicians to search for invariants of their topological equivalence. Under assumptions of different generality on the class of gradient-like flows under consideration, such classical invariants as the Leontovich–Mayer scheme, the Peixoto graph, the equipped Peixoto graph, the two-color Wang graph, the three-color Oshemkov–Sharko graph, the Fleitas circular scheme, etc. were obtained. Thus, the problem of classifying gradient-like flows on surfaces from the point of view of topological equivalence has been solved in an exhaustive way. In recent works by Kruglov, Malyshev, and Pochinka, it was proved that for gradient-like flows the topological equivalence classes coincide with the topological conjugacy ones. The obtained result allows us to use any invariants of their equivalence for topological conjugacy of gradient-like flows. The present study is a review of results on topological conjugacy of gradient-like flows on surfaces and efficient algorithms for its distinction, that is, algorithms whose running time is limited by some polynomial in the length of the input information.
- Subjects
ALGORITHMS; MATHEMATICIANS; POLYNOMIALS
- Publication
Journal of Mathematical Sciences, 2024, Vol 282, p378
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-024-07183-0