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.
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页码：461 / 473
页数：13
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