Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps

被引：34
|
作者：
Delshams, A. [1 ]
Gonchenko, S. V. [2 ]
Gonchenko, V. S. [2 ]
Lazaro, J. T. [1 ]
Sten'kin, O. [2 ]
机构：
[1] Univ Politecn Cataluna, Barcelona, Spain
[2] Inst Appl Math & Cybernet, Nizhnii Novgorod, Russia
来源：
NONLINEARITY | 2013年 / 26卷 / 01期
关键词：
HOMOCLINIC TANGENCIES; NEWHOUSE REGIONS; DIFFEOMORPHISMS; SYSTEMS; DIMENSION; CHAOS;
D O I：
10.1088/0951-7715/26/1/1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the dynamics and bifurcations of two-dimensional reversible maps with non-transversal heteroclinic cycles containing symmetric saddle fixed points. We consider one-parameter families of reversible maps unfolding the initial heteroclinic tangency and prove the existence of infinitely many sequences (cascades) of bifurcations and the birth of asymptotically stable, unstable and elliptic periodic orbits.
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页码：1 / 33
页数：33
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