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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2017, том 22, выпуск 7, страницы 840–850 (Mi rcd294)

Эта публикация цитируется в 2 статьях

Global Properties of Kovalevskaya Exponents

Andrzej J. Maciejewskia, Maria Przybylskab

a Janusz Gil Institute of Astronomy, University of Zielona Góra, ul. Licealna 9, 65-417, Zielona Góra, Poland
b Institute of Physics, University of Zielona Góra, ul. Licealna 9, PL-65–417, Zielona Góra, Poland

Аннотация: This paper contains a collection of properties of Kovalevskaya exponents which are eigenvalues of a linearization matrix of weighted homogeneous nonlinear systems along certain straight-line particular solutions. Relations in the form of linear combinations of Kovalevskaya exponents with nonnegative integers related to the presence of first integrals of the weighted homogeneous nonlinear systems have been known for a long time. As a new result other nonlinear relations between Kovalevskaya exponents calculated on all straight-line particular solutions are presented. They were obtained by an application of the Euler–Jacobi–Kronecker formula specified to an appropriate n-form in a certain weighted homogeneous projective space.

Ключевые слова: Kovalevskaya – Painlevé analysis, integrability, quasi-homogeneous systems.

MSC: 37J30, 34M45, 32A27

Поступила в редакцию: 17.08.2017
Принята в печать: 22.11.2017

Язык публикации: английский

DOI: 10.1134/S1560354717070061



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