About Integrability of the Degenerate System

Автор: Edneral Victor F.
Сборник: Computer Algebra in Scientific Computing
Серия: Lecture Notes in Computer Science
Том: 11661
Год издания: 2019
Место издания: Springer International Publishing Springer Nature Switzerland AG
Первая страница: 140
Последняя страница: 151
DOI: 10.1007/978-3-030-26831-2_10
Аннотация: 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.
Добавил в систему: Еднерал Виктор Федорович

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