Nilpotent centers of cubic systems

A. F. Andreev; I. A. Andreeva; L. V. Detchenya; T. V. Makovetskaya; A. P. Sadovskii

doi:10.1134/S0012266117080018

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
Affiliations:
1. Saint Petersburg State University
2. Peter the Great Polytechnic University
3. Yanka Kupala State University of Grodno
4. 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

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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.