Center conditions for polynomial Liénard systems
type: Item
instance of: scholarly article
title: Center conditions for polynomial Liénard systems
zbMATH Open document ID: 1392.34027
author: Jaume Giné
published in: Qualitative Theory of Dynamical Systems
publication date: 2018-04-03T00:00:00Z
full work available at URL: http://hdl.handle.net/10459.1/62957
review text: Consider the system \[ \begin{gathered} \dot x=y,\\ \dot y=-x-b_2x^2- b_3x^3- b_4 x^4- b_5 x^5- b_6 x^6-\\ (a_1 x+ a_2 x^2+ a_3 x^3+ a_4 x^4+ a_5 x^5+ a_6 x^6) y.\end{gathered}\tag{1} \] Theorem: Let \(V\) be the center variety of system (1). Then \[ V= \bigcup^3_{k=1} V(J_k), \] where \(J_1,J_2,J_3\) are prime ideals of the form \[ \begin{aligned} J_1 &= \langle 5b_2b_3- 3b_4, 2b^2_2b_3- 3b_5,3a_5- 2a_3 b^2_2,b_6, a_6, 3a_4- 5a_3 b_2, a_2- a_1b_2\rangle,\\ J_2 &= \langle a_3- a_1b_3, a_5- a_1b_5, a_6- a_1 b_6, a_4- a_1 b_4, a_2- a_1 b_2\rangle,\\ J_3 &= \langle b_2, b_4, b_6, a_6 a_4, a_2\rangle.\end{aligned} \]
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 6855268
zbMATH Keywords: center problem
zbMATH Keywords: analytic integrability
zbMATH Keywords: polynomial Liénard differential systems
zbMATH Keywords: Gröbner bases
zbMATH Keywords: decomposition in prime ideals
reviewed by: A. P. Sadovskiĭ
describes a project that uses: primdec
describes a project that uses: SINGULAR
MaRDI profile type: Publication
OpenAlex ID: W2403163037
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DOI: 10.1007/S12346-016-0202-3
description: scientific article; zbMATH DE number 6855268