Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field
Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field
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DOI：
10.1142/s0218127422501164
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Ting Chen;J. Llibre
中科院分区：
文献类型：
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作者：
Ting Chen;J. Llibre
本文研究了被直线[Formula：see text]分隔的连续分段二次Hamilton系统的全局动力学，其中这类系统在[Formula：see text]处有一个幂零中心，它来自于两个Hamilton系统的两个尖点的组合。通过Poincaré紧化，我们对这些系统的全局相图进行了分类。我们必须指出，像我们在这里所做的那样研究具有非基本奇异点的分段光滑系统中的中心焦点问题的作品是极其罕见的。
In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian systems separated by the straight line [Formula: see text], where these kinds of systems have a nilpotent center at [Formula: see text], which comes from the combination of two cusps of both Hamiltonian systems. By the Poincaré compactification we classify the global phase portraits of these systems. We must mention that it is extremely rare to find works studying the center-focus problem in piecewise smooth systems with nonelementary singular points as we did here.