The center problem and composition condition for Abel differential equations

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• 作者：Jaume Giné ; ; ^{gine@matematica.udl.cat" class="auth_mail" title="E-mail the corresponding author} ; Maite Grau ^{mtgrau@matematica.udl.cat" class="auth_mail" title="E-mail the corresponding author} ; Xavier Santallusia ^{xivaer@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 34C25 ; secondary ; 34C07
• 刊名：Expositiones Mathematicae
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：34
• 期：2
• 页码：210-222
• 全文大小：204 K

文摘

The classical Poincaré center-focus problem for planar polynomial systems of ordinary differential equations can be transformed, in certain particular cases, to the center problem of a trigonometric Abel differential equation. Several research papers focused on the study of the center problem for trigonometric Abel differential equations. Polynomial Abel differential equations are also considered in the literature as a model problem. In this work we make a survey of the most important results in this context and we provide the state of the art of several related conjectures. We give two new results on these conjectures.