A note on higher order Melnikov functions

被引：0

作者：

Jebrane A. ^{[1
]}

Zolładek H. ^{[2
]}

机构：

[1] Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université de Bourgogne, 21078 Dijon Cedex, 9 Av. Alain Savary

[2] Institute of Mathematics, University of Warsaw, 02-097 Warsaw

来源：

Qualitative Theory of Dynamical Systems | 2005年 / 6卷 / 2期

关键词：

Abelian integral; Higher order Melnikov integral;

D O I：

10.1007/BF02972677

中图分类号：

学科分类号：

摘要：

We present several classes of planar polynomial Hamilton systems and their polynomial perturbations leading to vanishing of the first Melnikov integral. We discuss the form of higher order Melnikov integrals. In particular, we present new examples where the second order Melnikov integral is not an Abelian integral.

引用

页码：273 / 287

页数：14

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