On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node

被引：1

作者：

Gonchenko, Serey V. ^{[1
]}

Gordeeva, Olga V. ^{[1
]}

Lukyanov, Valery I. ^{[1
]}

Ovsyannikov, Ivan I. ^{[1
,2
]}

机构：

[1] Nizhnii Novgorod State Univ, Nizhnii Novgorod 603000, Russia

[2] Univ London Imperial Coll Sci Technol & Med, London SW7 2AZ, England

来源：

REGULAR & CHAOTIC DYNAMICS | 2014年 / 19卷 / 04期

基金：

俄罗斯科学基金会; 英国工程与自然科学研究理事会;

关键词：

saddle-node; homoclinic tangency; Arnold tongues; SYSTEMS;

D O I：

10.1134/S1560354714040029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the main bifurcations of multidimensional diffeomorphisms having a nontransversal homoclinic orbit to a saddle-node fixed point. On a parameter plane we build a bifurcation diagram for single-round periodic orbits lying entirely in a small neighborhood of the homoclinic orbit. Also, a relation of our results to the well-known codimension one bifurcations of a saddle fixed point with a quadratic homoclinic tangency and a saddle-node fixed point with a transversal homoclinic orbit is discussed.

引用

页码：461 / 473

页数：13

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