Non-smooth quadratic centers defined in two arbitrary sectors

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• 作者：Isaac A. Garc&iacute ; a ; ^{garcia@matematica.udl.cat" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Non-smooth dynamics ; Center problem ; Periodic orbits ; Poincaré ; map
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：20 October 2016
• 年：2016
• 卷：289
• 期：Complete
• 页码：37-47
• 全文大小：438 K

文摘

In this paper we analyze the center–focus problem of some families of piecewise planar quadratic vector fields on two zones of R²${\mathbb{R}}^2$. The zones we consider are two unbounded sectors defined by an arbitrary angle α and a fixed vertex. We also assume that each vector field share a common weak focus singularity at the vertex of the boundary. We observe how the center variety depends on the angle α.