Asymptotic method for the investigation of m-frequency oscillation systems
We describe an asymptotic method for the integration of m-frequency oscillation systems of order 2n, analyze averaged equations in nonresonance and resonance cases, prove a theorem on the preservation of smooth p-dimensionai invariant tori under perturbation for any 0 ≤ p ≤ n, and indicate forms of...
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| Datum: | 1998 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4823 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511007435128832 |
|---|---|
| author | Samoilenko, A. M. Самойленко, А. М. Самойленко, А. М. |
| author_facet | Samoilenko, A. M. Самойленко, А. М. Самойленко, А. М. |
| author_sort | Samoilenko, A. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:15:12Z |
| description | We describe an asymptotic method for the integration of m-frequency oscillation systems of order 2n, analyze averaged equations in nonresonance and resonance cases, prove a theorem on the preservation of smooth p-dimensionai invariant tori under perturbation for any 0 ≤ p ≤ n, and indicate forms of decomposable m-frequency oscillation systems. |
| first_indexed | 2026-03-24T03:06:03Z |
| format | Article |
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| id | umjimathkievua-article-4823 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:06:03Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/1f/51ca032093192fa441eb6a55d9567f1f.pdf |
| spelling | umjimathkievua-article-48232020-03-18T21:15:12Z Asymptotic method for the investigation of m-frequency oscillation systems Асимптотический метод исследования $m$-частотных колебательных систем Samoilenko, A. M. Самойленко, А. М. Самойленко, А. М. We describe an asymptotic method for the integration of m-frequency oscillation systems of order 2n, analyze averaged equations in nonresonance and resonance cases, prove a theorem on the preservation of smooth p-dimensionai invariant tori under perturbation for any 0 ≤ p ≤ n, and indicate forms of decomposable m-frequency oscillation systems. Наведено асимптотичний метод інтегрування $m$-частотних коливних систем $2n$-го порядку, проведено аналіз усереднених рівнянь у нерезопаисному та резонансному випадках, доведено теорему збереження при збуренні гладких $p$-вимірних інваріантних торів при довільному $0 ≤ p ≤ n$, вказані види розщеплюваних $m$-частотних коливних систем. Institute of Mathematics, NAS of Ukraine 1998-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4823 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 10 (1998); 1366–1387 Український математичний журнал; Том 50 № 10 (1998); 1366–1387 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4823/6345 https://umj.imath.kiev.ua/index.php/umj/article/view/4823/6346 Copyright (c) 1998 Samoilenko A. M. |
| spellingShingle | Samoilenko, A. M. Самойленко, А. М. Самойленко, А. М. Asymptotic method for the investigation of m-frequency oscillation systems |
| title | Asymptotic method for the investigation of m-frequency oscillation systems |
| title_alt | Асимптотический метод исследования $m$-частотных колебательных
систем |
| title_full | Asymptotic method for the investigation of m-frequency oscillation systems |
| title_fullStr | Asymptotic method for the investigation of m-frequency oscillation systems |
| title_full_unstemmed | Asymptotic method for the investigation of m-frequency oscillation systems |
| title_short | Asymptotic method for the investigation of m-frequency oscillation systems |
| title_sort | asymptotic method for the investigation of m-frequency oscillation systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4823 |
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