Nilpotent centers of cubic systems
- Authors: Andreev A.F.1, Andreeva I.A.2, Detchenya L.V.3, Makovetskaya T.V.4, Sadovskii A.P.4
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Affiliations:
- Saint Petersburg State University
- Peter the Great Polytechnic University
- Yanka Kupala State University of Grodno
- Belarusian State University
- Issue: Vol 53, No 8 (2017)
- Pages: 975-980
- Section: Ordinary Differential Equations
- URL: https://journal-vniispk.ru/0012-2661/article/view/154497
- DOI: https://doi.org/10.1134/S0012266117080018
- ID: 154497
Cite item
Abstract
We present an explicit form of cubic systems with a nilpotent singular point of the focus or center type at the origin. A method for finding the focus quantities of such systems is indicated. Sufficient conditions for the existence of a nilpotent center for cubic systems are given. Cubic systems reducible to the Li´enard system are studied in detail.
About the authors
A. F. Andreev
Saint Petersburg State University
Email: irandr@inbox.ru
Russian Federation, St. Petersburg, 199034
I. A. Andreeva
Peter the Great Polytechnic University
Author for correspondence.
Email: irandr@inbox.ru
Russian Federation, St. Petersburg, 195251
L. V. Detchenya
Yanka Kupala State University of Grodno
Email: irandr@inbox.ru
Belarus, Grodno, 230023
T. V. Makovetskaya
Belarusian State University
Email: irandr@inbox.ru
Belarus, Minsk, 220030
A. P. Sadovskii
Belarusian State University
Email: irandr@inbox.ru
Belarus, Minsk, 220030
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