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Topological characterizations of Morse-Smale flows on surfaces and generic non-Morse-Smale flowsстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Kibkalo V., Yokoyama T.
- Журнал: Discrete and Continuous Dynamical Systems
- Том: 42
- Номер: 10
- Год издания: 2022
- Издательство: Dept. of Mathematics, Southwest Missouri State University
- Местоположение издательства: United States
- Первая страница: 4787
- Последняя страница: 4822
- Аннотация: https://doi.org/10.3934/dcds.2022072 It is known that C^1 Morse-Smale vector fields form an open dense subset in the space of vector fields on orientable closed surfaces and are structurally stable for any positive integer r. In particular, C^r Morse vector fields (i.e. Morse-Smale vector fields without limit cycles) form an open dense subset in the space of C^r gradient vector fields on orientable closed surfaces and are structurally stable. Therefore generic time evaluations of gradient flows on orientable closed surfaces (e.g. solutions of differential equations) are described by alternating sequences of Morse flows and instantaneous non-Morse gradient flows. To illustrate the generic transitions (e.g. bifurcations of singular points, transitions via heteroclinic separatrices), we characterize and list all generic non-Morse gradient flows. To construct such characterizations, we characterize isolated singular points of gradient flows on surfaces. In fact, such a singular point is a non-trivial finitely sectored singular point without elliptic sectors. Moreover, considering Morse-Smale flows as "generic gradient flows with limit cycles", we characterize and list all generic non-Morse-Smale flows.
- Добавил в систему: Кибкало Владислав Александрович