Topological aspects of dynamic systems
We give a definition of a minimal vector field whose singular elements are all hyperbolic. For a particular class of smooth manifolds we compute the number of minimal Morse-Smale vector fields. We find necessary and sufficient conditions for the L-equivalence of Morse-Smale vector fields. For Kupka-...
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| Date: | 1992 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7802 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512764924002304 |
|---|---|
| author | Sharko , V. V. Шарко, В. В. |
| author_facet | Sharko , V. V. Шарко, В. В. |
| author_sort | Sharko , V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-09-14T12:03:56Z |
| description | We give a definition of a minimal vector field whose singular elements are all hyperbolic. For a particular class of smooth manifolds we compute the number of minimal Morse-Smale vector fields. We find necessary and sufficient conditions for the L-equivalence of Morse-Smale vector fields. For Kupka-Smale fields we introduce a Lyapunov 1-form which we use to write down inequalities for the singular elements. |
| first_indexed | 2026-03-24T03:33:59Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-7802 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:33:59Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/60/e41d471eacb976b4b509dd6f836bbc60.pdf |
| spelling | umjimathkievua-article-78022023-09-14T12:03:56Z Topological aspects of dynamic systems Топологические аспекты динамических систем Sharko , V. V. Шарко, В. В. We give a definition of a minimal vector field whose singular elements are all hyperbolic. For a particular class of smooth manifolds we compute the number of minimal Morse-Smale vector fields. We find necessary and sufficient conditions for the L-equivalence of Morse-Smale vector fields. For Kupka-Smale fields we introduce a Lyapunov 1-form which we use to write down inequalities for the singular elements. Дано определение минимального векторного поля, особые элементы которого гиперболичны. Для некоторого класса гладких многообразий вычислено число минимальных векторных полей Морса—Смейла. Найдены необходимые и достаточные условия L-эквивалентности векторных полей Морса—Смейла. Для полей Купки — Смейла введена 1-форма Ляпунова, на основании которой выписаны неравенства для сингулярных элементов. Дано визначення мінімального векторного поля, особливі елементи якого гіперболічні. Для деякого класу гладких многовидів підраховано число мінімальних векторних полів Морса — Смейла. Знайдені необхідні і достатні умови L-еквівалентності мінімальних векторних полів Морса—Смейла. Для полів Купки — Смейла введена 1-форма Ляпунова, на основі якої виписані нерівності для сингулярних елементів. Institute of Mathematics, NAS of Ukraine 1992-02-04 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7802 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 1 (1992); 122-127 Український математичний журнал; Том 44 № 1 (1992); 122-127 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7802/9470 Copyright (c) 1992 V. V. Sharko |
| spellingShingle | Sharko , V. V. Шарко, В. В. Topological aspects of dynamic systems |
| title | Topological aspects of dynamic systems |
| title_alt | Топологические аспекты динамических систем |
| title_full | Topological aspects of dynamic systems |
| title_fullStr | Topological aspects of dynamic systems |
| title_full_unstemmed | Topological aspects of dynamic systems |
| title_short | Topological aspects of dynamic systems |
| title_sort | topological aspects of dynamic systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7802 |
| work_keys_str_mv | AT sharkovv topologicalaspectsofdynamicsystems AT šarkovv topologicalaspectsofdynamicsystems AT sharkovv topologičeskieaspektydinamičeskihsistem AT šarkovv topologičeskieaspektydinamičeskihsistem |