Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds
We investigate S1-invariant Hamiltonian systems on compact 4-dimensional symplectic manifolds with free symplectic action of a circle. We show that, in a rather general case, such systems generate ergodic flows of types (quasiperiodic and nilpotent) on their isoenergetic surfaces. We solve the probl...
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| Date: | 1997 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4991 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511183470067712 |
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| author | Parasyuk, I. O. Samoilenko, A. M. Парасюк, І. О. Самойленко, А. М. |
| author_facet | Parasyuk, I. O. Samoilenko, A. M. Парасюк, І. О. Самойленко, А. М. |
| author_sort | Parasyuk, I. O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:11Z |
| description | We investigate S1-invariant Hamiltonian systems on compact 4-dimensional symplectic manifolds with free symplectic action of a circle. We show that, in a rather general case, such systems generate ergodic flows of types (quasiperiodic and nilpotent) on their isoenergetic surfaces. We solve the problem of straightening of these flows. |
| first_indexed | 2026-03-24T03:08:50Z |
| format | Article |
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| id | umjimathkievua-article-4991 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:08:50Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/06/a9a40eee52151bc87affc9812b3ba906.pdf |
| spelling | umjimathkievua-article-49912020-03-18T21:22:11Z Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds Нільпотентні потоки S1-інваріантних гамільтонових систем на 4-вимірних симплектичних многовидах Parasyuk, I. O. Samoilenko, A. M. Парасюк, І. О. Самойленко, А. М. We investigate S1-invariant Hamiltonian systems on compact 4-dimensional symplectic manifolds with free symplectic action of a circle. We show that, in a rather general case, such systems generate ergodic flows of types (quasiperiodic and nilpotent) on their isoenergetic surfaces. We solve the problem of straightening of these flows. Досліджено S1-інваріантні гамільтонові системи на компактних 4-вимірних симплектичних многовидах з вільною симплектичною дією кола. Показано, що в досить загальній ситуації такі системи генерують на своїх ізоеиергетичних поверхнях ергодичні потоки двох типів — квазіперіодичні та нільпотентиі. Розв'язано задачу випрямлення цих потоків. Institute of Mathematics, NAS of Ukraine 1997-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4991 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 1 (1997); 122–140 Український математичний журнал; Том 49 № 1 (1997); 122–140 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4991/6681 https://umj.imath.kiev.ua/index.php/umj/article/view/4991/6682 Copyright (c) 1997 Parasyuk I. O.; Samoilenko A. M. |
| spellingShingle | Parasyuk, I. O. Samoilenko, A. M. Парасюк, І. О. Самойленко, А. М. Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds |
| title | Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds |
| title_alt | Нільпотентні потоки S1-інваріантних гамільтонових систем на 4-вимірних симплектичних многовидах |
| title_full | Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds |
| title_fullStr | Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds |
| title_full_unstemmed | Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds |
| title_short | Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds |
| title_sort | nilpotent flows of s1-invariant hamiltonian systems on 4-dimensional symplectic manifolds |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4991 |
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