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：

英国工程与自然科学研究理事会; 俄罗斯科学基金会;

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

共 50 条

[1] On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node
Serey V. Gonchenko
Olga V. Gordeeva
Valery I. Lukyanov
Ivan I. Ovsyannikov
Regular and Chaotic Dynamics, 2014, 19 : 461 - 473
[2] SADDLE-NODE BIFURCATIONS OF MULTIPLE HOMOCLINIC SOLUTIONS IN ODES
Lin, Xiao-Bin
Zhu, Changrong
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (04): : 1435 - 1460
[3] Homoclinic saddle-node bifurcations in singularly perturbed systems
Doelman A.
Hek G.
Journal of Dynamics and Differential Equations, 2000, 12 (1) : 169 - 216
[4] On Bifurcations of Three-Dimensional Diffeomorphisms with a Homoclinic Tangency to a “Neutral” Saddle Fixed Point
V. S. Gonchenko
I. I. Ovsyannikov
Journal of Mathematical Sciences, 2005, 128 (2) : 2774 - 2777
[5] Homoclinic saddle-node bifurcations and subshifts in a three-dimensional flow
Hek, G
Doelman, A
Holmes, P
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1998, 145 (04) : 291 - 329
[6] Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two
Bai, FS
Champneys, AR
DYNAMICS AND STABILITY OF SYSTEMS, 1996, 11 (04): : 325 - 346
[7] Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two
Tsinghua Univ, Beijing, China
Dyn Stab Syst, 4 (325-346):
[8] Saddle-node bifurcations for hyperbolic sets
Crovisier, S
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2002, 22 : 1079 - 1115
[9] Saddle-node bifurcations in the spectrum of HOCl
Weiss, J
Hauschildt, J
Grebenshchikov, SY
Düren, R
Schinke, R
Koput, J
Stamatiadis, S
Farantos, SC
JOURNAL OF CHEMICAL PHYSICS, 2000, 112 (01): : 77 - 93
[10] QUANTUM MANIFESTATIONS OF SADDLE-NODE BIFURCATIONS
BORONDO, F
ZEMBEKOV, AA
BENITO, RM
CHEMICAL PHYSICS LETTERS, 1995, 246 (4-5) : 421 - 426

← 1 2 3 4 5 →