About Integrability of the Degenerate System

We study integrability of an autonomous planar polynomial system of ODEs with a degenerate singular point at the origin depending on five parameters. By mean of the Power Geometry Method, this degenerated system is reduced to a non-degenerate form by the blow-up process. After, we search for the necessary conditions of local integrability by the normal form method. We look for the set of necessary conditions on parameters under which the original system is locally integrable near the degenerate stationary point. We found seven two-parametric families in the five-parameter space. Then first integrals of motion were found for six families. For the seventh family, we found the formal first integral. So, at least six of these families in parameters space are manifolds where the global integrability of the original system takes place.

Авторы
Редакторы
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Издательство
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Номер выпуска
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Язык
Английский
Страницы
140-151
Статус
Опубликовано
Подразделение
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Ссылка
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DOI
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Номер
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Том
11661 LNCS
Год
2019
Организации
  • 1 Skobeltsyn Institute of Nuclear Physics|Lomonosov Moscow State University
  • 2 Peoples’ Friendship University of Russia (RUDN University)
Ключевые слова
Computer Algebra; integrability; ordinary differential equations; power geometry; Resonant normal form
Дата создания
20.02.2020
Дата изменения
20.02.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/59525/