On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus
We investigate the problem of the existence of the Green–Samoilenko function for linear expansions of dynamical systems on a torus of the form $$\frac{{d\phi }}{{dt}} = a(\phi ),{\text{ }}C(\phi )\frac{{d\phi }}{{dt}} + \frac{1}{2}\dot C(\phi )x = A(\phi )x,$$ where C(ϕ) ∈ C′(T m; a) is a nondeg...
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| Date: | 2002 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4094 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510226773442560 |
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| author | Kulik, V. L. Stepanenko, N. V. Кулик, В. Л. Степаненко, Н. В. |
| author_facet | Kulik, V. L. Stepanenko, N. V. Кулик, В. Л. Степаненко, Н. В. |
| author_sort | Kulik, V. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:22:24Z |
| description | We investigate the problem of the existence of the Green–Samoilenko function for linear expansions of dynamical systems on a torus of the form $$\frac{{d\phi }}{{dt}} = a(\phi ),{\text{ }}C(\phi )\frac{{d\phi }}{{dt}} + \frac{1}{2}\dot C(\phi )x = A(\phi )x,$$ where C(ϕ) ∈ C′(T m; a) is a nondegenerate symmetric matrix. |
| first_indexed | 2026-03-24T02:53:38Z |
| format | Article |
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| id | umjimathkievua-article-4094 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:53:38Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e2/f93ebbd49017c307d98d2a15610325e2.pdf |
| spelling | umjimathkievua-article-40942020-03-18T20:22:24Z On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus Про властивість регулярності деяких лінійних розширень динамічних систем на торі Kulik, V. L. Stepanenko, N. V. Кулик, В. Л. Степаненко, Н. В. We investigate the problem of the existence of the Green–Samoilenko function for linear expansions of dynamical systems on a torus of the form $$\frac{{d\phi }}{{dt}} = a(\phi ),{\text{ }}C(\phi )\frac{{d\phi }}{{dt}} + \frac{1}{2}\dot C(\phi )x = A(\phi )x,$$ where C(ϕ) ∈ C′(T m; a) is a nondegenerate symmetric matrix. Досліджується питання існування функції Гріна - Самойленка для лінійних розширень динамічних систем на торі вигляду $$\frac{{d\phi }}{{dt}} = a(\phi ),{\text{ }}C(\phi )\frac{{d\phi }}{{dt}} + \frac{1}{2}\dot C(\phi )x = A(\phi )x,$$ з невиродженою симетричною матрицею $C(ϕ) ∈ C′(T_m; a)$. Institute of Mathematics, NAS of Ukraine 2002-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4094 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 4 (2002); 568-574 Український математичний журнал; Том 54 № 4 (2002); 568-574 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4094/4898 https://umj.imath.kiev.ua/index.php/umj/article/view/4094/4899 Copyright (c) 2002 Kulik V. L.; Stepanenko N. V. |
| spellingShingle | Kulik, V. L. Stepanenko, N. V. Кулик, В. Л. Степаненко, Н. В. On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus |
| title | On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus |
| title_alt | Про властивість регулярності деяких лінійних розширень динамічних систем на торі |
| title_full | On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus |
| title_fullStr | On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus |
| title_full_unstemmed | On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus |
| title_short | On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus |
| title_sort | on regularity of certain linear expansions of dynamical systems on a torus |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4094 |
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