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| CODIMENSION 3 BIFURCATIONS OF HOMOCLINIC ORBITS WITH ORBIT FLIPS AND INCLINATION FLIPS |
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Citation： |
SHUI Shuliang,ZHU Deming.CODIMENSION 3 BIFURCATIONS OF HOMOCLINIC ORBITS WITH ORBIT FLIPS AND INCLINATION FLIPS[J].Chinese Annals of Mathematics B,2004,25(4):555~566 |
| Page view： 1175
Net amount： 918 |
Authors： |
SHUI Shuliang; ZHU Deming |
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| Abstract： |
The homoclinic bifurcations in four dimensional vector fields are investigated by
setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is nonprincipal
in the meanings that its positive semi-orbit takes orbit flip and its unstable
foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence
of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold
periodic orbit and three-fold periodic orbit are also obtained. |
Keywords： |
Bifurcation, Homoclinic orbit, Orbit flip, Inclination flip, Periodic orbit |
Classification： |
37C29, 34C23, 34C37 |
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