Bifurcations of Cubic Homoclinic Tangencies in Two-dimensional Symplectic Maps

被引：4
|
作者：
Gonchenko, M. [1 ]
Gonchenko, S. [2 ]
Ovsyannikov, I. [3 ]
机构：
[1] Univ Barcelona, Dept Math & Informat, E-08007 Barcelona, Spain
[2] NI Lobachevsky Nizhny Novgorod Univ, Nizhnii Novgorod, Russia
[3] Univ Bremen, Fachbereich Math & Informat, D-28359 Bremen, Germany
来源：
MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2017年 / 12卷 / 01期
关键词：
symplectic map; homoclinic tangency; cubic Henon map; bifurcation; 1:4 resonance; AREA-PRESERVING MAPS; PERIODIC-ORBITS; HENON MAPS; SYSTEMS; DIFFEOMORPHISMS; RESONANCES; DYNAMICS; ISLANDS; POINTS;
D O I：
10.1051/mmnp/201712104
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different first return maps derived to diverse conservative cubic Henon maps with quite different bifurcation diagrams. In this way, we establish the structure of bifurcations of periodic orbits in two parameter general unfoldings generalizing to the conservative case the results previously obtained for the dissipative case. We also consider the problem of 1:4 resonance for the conservative cubic Henon maps.
引用
收藏
页码：41 / 61
页数：21
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