Separatrix Splitting in 3D Volume-Preserving Maps

被引:7
|
作者
Lomeli, Hector E. [1 ]
Ramirez-Ros, Rafael [2 ]
机构
[1] Inst Tecnol Autonomo Mexico, Dept Math, Mexico City 01000, DF, Mexico
[2] Univ Politecn Cataluna, Dept Matemat Aplicada 1, E-08028 Barcelona, Spain
来源
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2008年 / 7卷 / 04期
关键词
separatrix splitting; volume-preserving maps; primary heteroclinic set; Melnikov method; bifurcations;
D O I
10.1137/080713173
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We construct a family of integrable volume-preserving maps in R-3 with a two-dimensional heteroclinic connection of spherical shape between two fixed points of saddle-focus type. In other contexts, such structures are called Hill's spherical vortices or spheromaks. We study the splitting of the separatrix under volume-preserving perturbations using a discrete version of the Melnikov method. First, we establish several properties under general perturbations. For instance, we bound the topological complexity of the primary heteroclinic set in terms of the degree of some polynomial perturbations. We also give a sufficient condition for the splitting of the separatrix under some entire perturbations. A broad range of polynomial perturbations verify this sufficient condition. Finally, we describe the shape and bifurcations of the primary heteroclinic set for a specific perturbation.
引用
收藏
页码:1527 / 1557
页数:31
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