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A Linear Estimate of the Number of Limit Cycles for A Piecewise Smooth Near-Hamiltonian System
Qualitative Theory of Dynamical Systems ( IF 1.9 ) Pub Date : 2020-05-25 , DOI: 10.1007/s12346-020-00398-x
Xiaoyan Chen , Maoan Han

In this paper, we study Poincaré bifurcation of limit cycles from a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop round the origin. By using the Melnikov function method, we give an estimation of the number of limit cycles which bifurcate from the period annulus between the center and the homoclinic loop under the piecewise polynomial perturbations of degree n. This result confirms a conjecture.

中文翻译:

分段光滑近哈密顿系统极限环数的线性估计

在本文中,我们研究了一个以线性线性哈密顿系统为中心的极限环的庞加莱分叉,该系统以原点为中心,并以原点为中心的同斜环。通过使用梅尔尼科夫函数方法,我们给出了在次数为n的分段多项式摄动情况下,从中心与同斜环之间的周期环分叉的极限环数的一个估计。这个结果证实了一个推测。
更新日期:2020-05-25
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