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| Bifurcation Analysis of the Multiple FlipsHomoclinic Orbit |
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Citation： |
Tiansi ZHANG,Deming ZHU.Bifurcation Analysis of the Multiple FlipsHomoclinic Orbit[J].Chinese Annals of Mathematics B,2015,36(1):91~104 |
| Page view： 1575
Net amount： 1414 |
Authors： |
Tiansi ZHANG; Deming ZHU; |
Foundation： |
the National Natural Science Foundation of China (No. 11126097). |
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| Abstract： |
A high-codimension homoclinic bifurcation is considered with one orbit flip
and two inclination flips accompanied by resonant principal eigenvalues. A local active
coordinate system in a small neighborhood of homoclinic orbit is introduced. By analysis of
the bifurcation equation, the authors obtain the conditions when the original flip homoclinic
orbit is kept or broken. The existence and the existence regions of several double periodic
orbits and one triple periodic orbit bifurcations are proved. Moreover, the complicated
homoclinic-doubling bifurcations are found and expressed approximately. |
Keywords： |
Orbit flip, Inclination flips, Homoclinic orbit, Resonance |
Classification： |
37C29, 34C23, 34C37 |
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