Normal forms near a symmetric planar saddle connection

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• 作者：Jeroen Wynen ^{jeroen.wynen@uhasselt.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34C20 ; 37G05 ; 37C10
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：260
• 期：10
• 页码：7606-7633
• 全文大小：438 K

文摘

The present paper studies vector fields of the form $\dot{x}=(q/2+O(1-x^2))(1-x^2)+O(y)$, b4505b4">$\dot{y}=(px+O(1-x^2))y+O(y^2)$, which contain a separatrix connection between hyperbolic saddles with opposite eigenvalues where the connection is fixed. Smooth semi-local normal forms are provided in vicinity of the connection, both in the resonant and non-resonant case. First, a formal conjugacy is constructed near the separatrix. Then, a smooth change of coordinates is realized by generalizing known local results near the hyperbolic points.