Weak type heterodimensional cycle bifurcation with orbit-flip  

作　　者：LU QiuYing ZHU DeMing GENG 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》2011年第6期1175-1196,共22页中国科学：数学（英文版）

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.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：local moving frame weak heterodimensional cycle orbit-flip 

分 类 号：O175.1[理学—数学] TN710.01[理学—基础数学]