Nilpotent centers of cubic systems


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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.

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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