An upper bound of the index of an equilibrium point in the plane

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• 作者：Jaume Llibre ; Jos¨¦ Mart¨ªnez-Alfaro
• 关键词：Index ; Planar differential systems ; Gradient systems ; Hamiltonian systems
• 刊名：Journal of Differential Equations
• 出版年：2012
• 出版时间：15 October, 2012
• 年：2012
• 卷：253
• 期：8
• 页码：2460-2473
• 全文大小：314 K

文摘

We give an upper bound of the index of an isolated equilibrium point of a vector field in the plane. The vector field is decomposed in gradient and Hamiltonian components. This decomposition is related with the Loewner vector field. Associated to this decomposition we consider the set ¦° where the gradient and Hamiltonian components are linearly dependent. The number of branches of ¦° starting at the equilibrium point determines the upper bound of the index.