Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips  

作　　者：SHUI Shuliang & ZHU Deming College of Mathematics and Physics, Zhejiang Normal University, Jinhua 321004, China Department of Mathematics, East China Normal University, Shanghai 200062, China 

出　　处：《Science China Mathematics》2005年第2期248-260,共13页中国科学：数学（英文版）

基　　金：This paper was completed when the first author was visiting East China Normal University.This work was supported by the National Natural Science Foundation of China(Grant No.10071022).

摘　　要：Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1 -periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.

关 键 词：bifurcation  HOMOCLINIC orbit  non-resonance  INCLINATION flip  1-periodic orbit. 

分 类 号：O183[理学—数学]