The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I
On the basis of the geometric ideas of Poincaré and Mel'nikov, we study sufficient criteria of the transversal splitting of heteroclinic separatrix manifolds of slowly perturbed nonlinear dynamical systems with a small parameter. An example of adiabatic invariance breakdown is considered fo...
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| Date: | 1993 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5975 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512198421381120 |
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| author | Prykarpatsky, A. K. Samoilenko, A. M. Timchishin, O. Ya. Прикарпатський, А. К. Самойленко, А. М. Тимчишин, О. Ф. |
| author_facet | Prykarpatsky, A. K. Samoilenko, A. M. Timchishin, O. Ya. Прикарпатський, А. К. Самойленко, А. М. Тимчишин, О. Ф. |
| author_sort | Prykarpatsky, A. K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:22:20Z |
| description | On the basis of the geometric ideas of Poincaré and Mel'nikov, we study sufficient criteria of the transversal splitting of heteroclinic separatrix manifolds of slowly perturbed nonlinear dynamical systems with a small parameter. An example of adiabatic invariance breakdown is considered for a system on a plane. |
| first_indexed | 2026-03-24T03:24:58Z |
| format | Article |
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| id | umjimathkievua-article-5975 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:24:58Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ee/91ea624c6a298dff46ab36e472ae8aee.pdf |
| spelling | umjimathkievua-article-59752020-03-19T09:22:20Z The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I Геометричний аналіз Пуанкаре і Мельникова трансверсального розщеплення сепаратрисних многовидів повільно збурених нелінійних динамічних систем. I Prykarpatsky, A. K. Samoilenko, A. M. Timchishin, O. Ya. Прикарпатський, А. К. Самойленко, А. М. Тимчишин, О. Ф. On the basis of the geometric ideas of Poincaré and Mel'nikov, we study sufficient criteria of the transversal splitting of heteroclinic separatrix manifolds of slowly perturbed nonlinear dynamical systems with a small parameter. An example of adiabatic invariance breakdown is considered for a system on a plane. На основі розвитку геометричних ідей Пуанкаре - Мельникова вивчаються достатні критерії трансверсального розщеплення тетерок лінічних сепарагрисних многовидів повільно збурених нелінійних динамічних систем з малим параметром. Розглянуто приклад руйнування адіабатичної інваріантності водній системі на площині. Institute of Mathematics, NAS of Ukraine 1993-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5975 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 12 (1993); 1668–1681 Український математичний журнал; Том 45 № 12 (1993); 1668–1681 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5975/8633 https://umj.imath.kiev.ua/index.php/umj/article/view/5975/8634 Copyright (c) 1993 Prykarpatsky A. K.; Samoilenko A. M.; Timchishin O. Ya. |
| spellingShingle | Prykarpatsky, A. K. Samoilenko, A. M. Timchishin, O. Ya. Прикарпатський, А. К. Самойленко, А. М. Тимчишин, О. Ф. The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I |
| title | The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I |
| title_alt | Геометричний аналіз Пуанкаре і Мельникова трансверсального розщеплення сепаратрисних многовидів повільно збурених нелінійних динамічних систем. I |
| title_full | The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I |
| title_fullStr | The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I |
| title_full_unstemmed | The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I |
| title_short | The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I |
| title_sort | poincare-mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. i |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5975 |
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