Vector fields with a given set of singular points
Theorems on the existence of vector fields with given sets of indexes of isolated singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a two-dimensional manifold, an index of an isolated singular point o...
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5135 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511336788656128 |
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| author | Prishlyak, O. O. Пришляк, О. О. |
| author_facet | Prishlyak, O. O. Пришляк, О. О. |
| author_sort | Prishlyak, O. O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:25:28Z |
| description | Theorems on the existence of vector fields with given sets of indexes of isolated singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a two-dimensional manifold, an index of an isolated singular point of the gradient field is not greater than one. |
| first_indexed | 2026-03-24T03:11:17Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5135 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:11:17Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/93/82942954b01b345b7239dd9e642b8d93.pdf |
| spelling | umjimathkievua-article-51352020-03-18T21:25:28Z Vector fields with a given set of singular points Векторные поля с заданным набором особых точек Prishlyak, O. O. Пришляк, О. О. Theorems on the existence of vector fields with given sets of indexes of isolated singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a two-dimensional manifold, an index of an isolated singular point of the gradient field is not greater than one. Доведені теореми про існування векторних полів, які мають даний набір індексів ізольованих особливих точок для замкнених миоговидів, пар многовидів, многовидів з краєм і градієнтних полів. Доведено, що індекс ізольованої особливої точки поля градієнта на двовимірному много-виді не більший за 1 Institute of Mathematics, NAS of Ukraine 1997-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5135 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 10 (1997); 1373–1384 Український математичний журнал; Том 49 № 10 (1997); 1373–1384 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5135/6966 https://umj.imath.kiev.ua/index.php/umj/article/view/5135/6967 Copyright (c) 1997 Prishlyak O. O. |
| spellingShingle | Prishlyak, O. O. Пришляк, О. О. Vector fields with a given set of singular points |
| title | Vector fields with a given set of singular points |
| title_alt | Векторные поля с заданным набором особых точек |
| title_full | Vector fields with a given set of singular points |
| title_fullStr | Vector fields with a given set of singular points |
| title_full_unstemmed | Vector fields with a given set of singular points |
| title_short | Vector fields with a given set of singular points |
| title_sort | vector fields with a given set of singular points |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5135 |
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