Weak type heterodimensional cycle bifurcation with orbit-flip

查看全文 作　　者：LU [1]QiuYing;ZHU [2]DeMing;GENG [3]FengJie

机构地区：[1]Department of Mathematics, Zhejiang Sci- Tech University, Hangzhou 310018, China;[2]Department of Mathematics, East China Normal University, Shanghai 200241, China;[3]School of Information Engineering, China University of Geosciences, Beijing 100083, China

出　　处：《Science China Mathematics》索引2011年第54卷第6期,共22页

基　　金：supported by the Foundation of Zhejiang Sci-Tech University (ZSTU)(Grant No. 11432732611046);National Natural Science Foundation of China (Grant No. 10671069) 摘　　要：In this paper, we study the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit by using the local moving frame approach. For the first two subcases, we present the sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. Based on the bifurcation analysis, the bifurcation surfaces and the existence regions are located. And for the third subcase, we theoretically established both the coexistence condition for the homoclinic loop and the periodic orbit and the coexistence condition for the persistent heterodimensional cycle and multiple periodic orbits due to the weak type of the transversal heteroclinic orbit. Moreover, an analytical example is presented for this subcase. 关键词：周期分岔同宿轨道弱型翻转周期轨道异宿轨道充分条件分岔分析

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Weak type heterodimensional cycle bifurcation with orbit-flip

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