On dynamics and bifurcations of area-preserving maps with homoclinic tangencies

被引：10

作者：

Delshams, Amadeu ^{[1
]}

Gonchenko, Marina ^{[2
]}

Gonchenko, Sergey ^{[3
]}

机构：

[1] Univ Politecn Cataluna, Dept Matemat Aplicada 1, E-08028 Barcelona, Spain

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

[3] Nizhnii Novgorod State Univ, Inst Appl Math & Cybernet, Nizhnii Novgorod 603005, Russia

来源：

NONLINEARITY | 2015年 / 28卷 / 09期

基金：

俄罗斯科学基金会;

关键词：

homoclinic tangency; area preserving mapping; bifurcation; ELLIPTIC ISLANDS; 2-DIMENSIONAL DIFFEOMORPHISMS; SYSTEMS; ISLES;

D O I：

10.1088/0951-7715/28/9/3027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of elliptic periodic orbits. In particular, we find conditions for such maps to have infinitely many generic (KAM-stable) elliptic periodic orbits of all successive periods starting at some number.

引用

页码：3027 / 3071

页数：45

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[1] On bifurcations of area-preserving and nonorientable maps with quadratic homoclinic tangencies
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