Abstract
We consider the center–focus problem for a polynomial Liénard system (polynomial vector field \((y-F(x)){\partial }/{\partial x}-\tilde {g}(x){\partial }/{\partial y}\)) at the monodromic singular point \((0,0) \). We obtain a description of the semialgebraic set of centers in the space of coefficients of the polynomials \((F(x)=\int \nolimits _0^x\tilde {f}(\tau )\thinspace d\tau \), \(G(x)=\int \nolimits _0^x\tilde {g }(\tau )\thinspace d\tau )\) based on eliminating the parameters \(A\), \(B \), and \(C \) from the composition condition \(F=B(A) \), \(G=C(A)\).
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Borukhov, V.T. Algebraic Criterion for the Existence of a Center at a Monodromic Singular Point of a Polynomial Liénard System. Diff Equat 58, 1008–1020 (2022). https://doi.org/10.1134/S001226612208002X
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DOI: https://doi.org/10.1134/S001226612208002X