Vladislav D. Galkin, Elena V. Nozdrinova, Olga V. Pochinka
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引用次数: 0
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.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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