Algebraic Criterion for the Existence of a Center at a Monodromic Singular Point of a Polynomial Liénard System

We consider the center–focus problem for a polynomial Liénard system (polynomial vector field ) at the monodromic singular point . We obtain a description of the semialgebraic set of centers in the space of coefficients of the polynomials , based on eliminating the parameters , , and from the compos...

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Bibliographic Details
Published in:Differential equations 2022-08, Vol.58 (8), p.1008-1020
Main Author: Borukhov, V. T.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Differential equations
Fields (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Polynomials
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Summary:We consider the center–focus problem for a polynomial Liénard system (polynomial vector field ) at the monodromic singular point . We obtain a description of the semialgebraic set of centers in the space of coefficients of the polynomials , based on eliminating the parameters , , and from the composition condition , .
ISSN:0012-2661
1608-3083
DOI:10.1134/S001226612208002X