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| Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip |
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Citation： |
Shuliang SHUI,Deming ZHU.Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip[J].Chinese Annals of Mathematics B,2006,27(6):657~674 |
| Page view： 1232
Net amount： 766 |
Authors： |
Shuliang SHUI; Deming ZHU |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10471087) and the Zhejiang
Provincial Natural Science Foundation of China (No.Y605044). |
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| Abstract： |
Heteroclinic bifurcations in four dimensional vector fields are investigated by
setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a
principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The
existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic
orbit and 1-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic
orbit is also obtained. |
Keywords： |
Bifurcation, Heteroclinic loop, Non-resonance, Orbit flip, Periodic orbit |
Classification： |
34C37, 37C29, 34C23 |
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