Codimension-4 Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips  

作　　者：Tian Si ZHANG De Ming ZHU 

机构地区：[1]College of Science, University of Shanghai for Science and Technology [2]Department of Mathematics, East China Normal University

出　　处：《Acta Mathematica Sinica,English Series》2015年第8期1359-1366,共8页数学学报（英文版）

基　　金：Supported by NSFC(Grant No.11126097)

摘　　要：The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit.Local active coordinate system is introduced to construct the Poincar′e returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the perioddoubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2n-homoclinic orbits.The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit.Local active coordinate system is introduced to construct the Poincar′e returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the perioddoubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2n-homoclinic orbits.

关 键 词：Orbit flip inclination flip RESONANT homoclinic-doubling bifurcations 

分 类 号：O175[理学—数学]