Nilpotent bi-center in continuous piecewise $${\mathbb Z}_2$$-equivariant cubic polynomial Hamiltonian systems
Nilpotent bi-center in continuous piecewise $${\mathbb Z}_2$$-equivariant cubic polynomial Hamiltonian systems
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DOI：
10.1007/s11071-022-07631-z
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发表时间：
2022-06
影响因子：
5.6
通讯作者：
Ting Chen;Shimin Li;J. Llibre
中科院分区：
文献类型：
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作者：
Ting Chen;Shimin Li;J. Llibre
平面微分系统中心的分类问题是平面微分系统理论中的一个经典而又困难的问题。在这里，我们分类的整体相图在庞加莱盘的类连续分段微分系统由一条直线分开，并形成两个三次Hamilton系统的幂零双中心在。证明我们的结果的主要工具是庞加莱紧化，指数理论，和理论的符号列表确定的确切数目的真实的根或负真实的根的真实的多项式在一个变量。
One of the classical and difficult problems in the theory of planar differential systems is to classify their centers. Here we classify the global phase portraits in the Poincaré disk of the class continuous piecewise differential systems separated by one straight line and formed by two cubic Hamiltonian systems with nilpotent bi-center at. The main tools for proving our results are the Poincaré compactification, the index theory, and the theory of sign lists for determining the exact number of real roots or negative real roots of a real polynomial in one variable.