Limit cycles appearing after perturbation of certain multidimensional vector fields

被引：0
作者：
Leszczyński P. [1 ]
Zoła̧dek H. [1 ]
机构：
[1] Institute of Mathematics, University of Warsaw, 02-097 Warsaw
来源：
Journal of Dynamics and Differential Equations | 2001年 / 13卷 / 4期
关键词：
Limit cycles; Normal hyperbolicity; Poincaré-Pontriagin-Melnikov integral;
D O I：
10.1023/A:1012858008962
中图分类号：
学科分类号：
摘要：
Let an unperturbed multidimensional polynomial vector field have an invariant plane L and let the system restricted to this plane be Hamiltonian with a quadratic Hamilton function. Now take a polynomial perturbation of this system. The new system has an invariant surface close to L and the system restricted to it has a certain number of limit cycles. We strive to estimate this number. The linearization of this problem leads to estimation of the number of zeros of certain integral, which is a generalization of the abelian integral. We estimate this number of zeros by C1 + C2n, where n is the degree of the perturbation. © 2001 Plenum Publishing Corporation.
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页码：689 / 709
页数：20
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