The number of limit cycles of polynomial deformations of a Hamiltonian vector field
The number of limit cycles of polynomial deformations of a Hamiltonian vector field
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DOI：
10.1017/s0143385700005721
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发表时间：
1990-09
影响因子：
0.9
通讯作者：
P. Mardešić
中科院分区：
文献类型：
--
作者：
P. Mardešić
摘要 我们证明了哈密顿矢量场的 n 次小非保守多项式变形的极限环数量的最低上限为 n − 1。因此，尖点的一般 n 参数变形的极限环数量的最低上限为 n − 1。
Abstract We prove that the lowest upper bound for the number of limit cycles of small nonconservative polynomial deformations of degree n of the Hamiltonian vector field is n − 1. A consequence is that the lowest upper bound for the number of limit cycles of generic n-parameter deformations of cusps is n − 1.