A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus
Under the assumption that a linear homogeneous system defined on the direct product of a torus and a Euclidean space is exponentially dichotomous on the semiaxes, we obtain a condition for the existence of a unique Green–Samoilenko function for the problem of invariant torus. We find an expression f...
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4277 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865791395863724032 |
|---|---|
| author | Boichuk, О. A. Бойчук, А. А. Бойчук, А. А. |
| author_facet | Boichuk, О. A. Бойчук, А. А. Бойчук, А. А. |
| author_institution_txt_mv | [
{
"author": "А. А. Бойчук",
"institution": null
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| author_sort | Boichuk, О. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:45Z |
| description | Under the assumption that a linear homogeneous system defined on the direct product of a torus and a Euclidean space is exponentially dichotomous on the semiaxes, we obtain a condition for the existence of a unique Green–Samoilenko function for the problem of invariant torus. We find an expression for this function in terms of projectors that determine the dichotomy on the semiaxes. |
| first_indexed | 2026-03-24T02:56:30Z |
| format | Article |
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| id | umjimathkievua-article-4277 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:56:30Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a2/5310b0f04b8e4aeb892438a517e927a2.pdf |
| spelling | umjimathkievua-article-42772020-03-18T20:25:45Z A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus Условие существования единственной функции Грина - Самойленко задачи об инвариантном торе Boichuk, О. A. Бойчук, А. А. Бойчук, А. А. Under the assumption that a linear homogeneous system defined on the direct product of a torus and a Euclidean space is exponentially dichotomous on the semiaxes, we obtain a condition for the existence of a unique Green–Samoilenko function for the problem of invariant torus. We find an expression for this function in terms of projectors that determine the dichotomy on the semiaxes. У припущенні, що лінійна однорідна система, яка визиачена на прямому добутку тора та евклідового простору, є експоиенціально-дихотомічною на півосях, отримано умову ісиування единої фуикції Гріна - Самойленка задачі про інваріантний тор та знайдено її вираз через проектори, що визначають дихотомію на півосях. Institute of Mathematics, NAS of Ukraine 2001-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4277 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 4 (2001); 556-559 Український математичний журнал; Том 53 № 4 (2001); 556-559 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4277/5258 https://umj.imath.kiev.ua/index.php/umj/article/view/4277/5259 Copyright (c) 2001 Boichuk О. A. |
| spellingShingle | Boichuk, О. A. Бойчук, А. А. Бойчук, А. А. A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus |
| title | A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus |
| title_alt | Условие существования единственной функции Грина - Самойленко задачи об инвариантном торе |
| title_full | A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus |
| title_fullStr | A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus |
| title_full_unstemmed | A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus |
| title_short | A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus |
| title_sort | condition for the existence of a unique green–samoilenko function for the problem of invariant torus |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4277 |
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