Higher order limit cycle bifurcations from non-degenerate centers
Higher order limit cycle bifurcations from non-degenerate centers
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DOI：
10.1016/j.amc.2012.02.044
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
J. Giné
中科院分区：
文献类型：
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作者：
J. Giné
在庞加莱-李雅普诺夫常数的计算中出现的计算问题以及它们的功能独立数的确定导致最近的工作只考虑这些常数的最低项。本文改进了在这个方向上得到的多项式系统xstec =-y+Pn（x，y），ystec =x+Qn（x，y）的结果，其中Pn，Qn是n次齐次多项式.本文利用中心分歧估计了不同n值下唯一的焦点-中心型奇点的循环性，并与文献[15]中的猜想结果进行了比较。
The computational problems which appear in the computation of the Poincaré–Liapunov constants and the determination of their functionally independent number has led in recent works to consider only the lowest terms of these constants. In this work we improve the results obtained in this direction for polynomials systems of the form x˙=-y+Pn(x,y),y˙=x+Qn(x,y), where Pnand Qnare a homogeneous polynomial of degree n. We use center bifurcation to estimate the cyclicity of a unique singular point of focus-center type for different values of n and compare with the results given by the conjecture presented in [15].