On the Gröbner Basis of the Ideal of Lyapunov Quantities of the Kukles System-Reference-Cited by-同舟云学术

On the Gröbner Basis of the Ideal of Lyapunov Quantities of the Kukles System

Published:2023-02-15 Issue:2 Volume:59 Page:170-182
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Rudenok A. E¹,Vasilevich M. N¹

Affiliation:

1. Belarusian State University, Minsk, 220030, Belarus

Abstract

The center problem and the cyclicity of singular points of the Kukles system are studied. The necessary conditions for the center at the origin are obtained as the variety of the ideal of Lyapunov quantities calculated by direct solution of the polynomial system whose left-hand sides form the Gröbner basis of the ideal. This ideal is also used to calculate the cyclicity of the centers and foci of the system. A theorem is proved that allows one to find the cyclicity of the centers of polynomial systems by using its Gröbner basis instead of the ideal of Lyapunov quantities.

Publisher

The Russian Academy of Sciences

Reference19 articles.

1. Куклес И.С. О некоторых случаях отличия фокуса от центра // Докл. АН СССР. 1944. Т. 42. № 5. С. 208-211.

2. Gine J. Center conditions for generalized polynomial Kukles systems // Commun. Pure Appl. Anal. 2017. V. 16. № 2. P. 417-426.

3. Lloyd N.G., Pearson J.M. Computing centre conditions for certain cubic systems // J. Comp. Appl. Math. 1992. V. 40. № 3. P. 323-336.

4. Садовский А.П. Решение проблемы центра и фокуса для кубической системы нелинейных колебаний // Дифференц. уравнения. 1997. Т. 33. № 2. С. 236-244.

5. Садовский А.П. Кубические системы нелинейных колебаний с семью предельными циклами // Дифференц. уравнения. 2003. Т. 39. № 4. С. 472-481.