Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips

被引：0
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作者：
Shuliang Shui
Deming Zhu
机构：
[1] Zhejiang Normal University,College of Mathematics and Physics
[2] East China Normal University,Department of Mathematics
来源：
Science in China Series A: Mathematics | 2005年 / 48卷
关键词：
bifurcation; homoclinic orbit; non-resonance; inclination flip; 1-periodic orbit;
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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.
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页码：248 / 260
页数：12
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