Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori
A symplectic manifold is considered under the assumption that a smooth symplectic action of a commutative Lie group with compact coisotropic orbits is defined on it. The problem of existence of variables of the action-angle type is investigated with a view to giving a detailed description of flows i...
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5785 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512008968863744 |
|---|---|
| author | Parasyuk, I. O. Парасюк, И. О. Парасюк, И. О. |
| author_facet | Parasyuk, I. O. Парасюк, И. О. Парасюк, И. О. |
| author_sort | Parasyuk, I. O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:17:59Z |
| description | A symplectic manifold is considered under the assumption that a smooth symplectic action of a commutative Lie group with compact coisotropic orbits is defined on it. The problem of existence of variables of the action-angle type is investigated with a view to giving a detailed description of flows in Hamiltonian systems with invariant Hamiltonians. We introduce the notion of a nonresonance symplectic structure for which the problem of recognition of resonance and nonresonance tori is solved. |
| first_indexed | 2026-03-24T03:21:58Z |
| format | Article |
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| id | umjimathkievua-article-5785 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:21:58Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/cc/04e26fc142049404bcfdefaa388f33cc.pdf |
| spelling | umjimathkievua-article-57852020-03-19T09:17:59Z Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori Переменные типа действие-угол на симплектических многообразиях, расслоенных коиэотропными торами Parasyuk, I. O. Парасюк, И. О. Парасюк, И. О. A symplectic manifold is considered under the assumption that a smooth symplectic action of a commutative Lie group with compact coisotropic orbits is defined on it. The problem of existence of variables of the action-angle type is investigated with a view to giving a detailed description of flows in Hamiltonian systems with invariant Hamiltonians. We introduce the notion of a nonresonance symplectic structure for which the problem of recognition of resonance and nonresonance tori is solved. Розглянуто симплектичний многовид у припущенні, що на ньому визначено симгілектичну дію комутативної групи Лі з компактними коізотропними орбітами. З метою детального опису потоків гамільтонових систем з інваріантними гамільтоніанами досліджено проблему існування змінних типу дія-кут. Впроваджено поняття нерезонансної симплектичної структури, для якої розв’язано задачу розпізнання резонансних та нерезонансних торів. Institute of Mathematics, NAS of Ukraine 1993-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5785 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 1 (1993); 77–85 Український математичний журнал; Том 45 № 1 (1993); 77–85 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5785/8254 https://umj.imath.kiev.ua/index.php/umj/article/view/5785/8255 Copyright (c) 1993 Parasyuk I. O. |
| spellingShingle | Parasyuk, I. O. Парасюк, И. О. Парасюк, И. О. Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori |
| title | Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori |
| title_alt | Переменные типа действие-угол на симплектических многообразиях, расслоенных коиэотропными торами |
| title_full | Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori |
| title_fullStr | Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori |
| title_full_unstemmed | Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori |
| title_short | Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori |
| title_sort | variables of the action-angle type on symplectic manifolds stratified by coisotropic tori |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5785 |
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