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| Bifurcation of Homoclinic Orbits with Saddle-Center Equilibrium |
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Citation： |
Xingbo LIU,Xianlong FU,Deming ZHU.Bifurcation of Homoclinic Orbits with Saddle-Center Equilibrium[J].Chinese Annals of Mathematics B,2007,28(1):81~92 |
| Page view： 1159
Net amount： 819 |
Authors： |
Xingbo LIU; Xianlong FU;Deming ZHU |
Foundation： |
Project supported by the National Natural Science Foundation |
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| Abstract： |
In this paper, the authors develop new global perturbation techniques for detecting the persistence of transversal homoclinic orbits in a more general nondegenerated system with action-angle variable. The unperturbed system is assumed to have saddlecenter type equilibrium whose stable and unstable manifolds intersect in one dimensional manifold, and does not have to be completely integrable or near-integrable. By constructing local coordinate systems near the unperturbed homoclinic orbit, the conditions of existence of transversal homoclinic orbit are obtained, and the existence of periodic orbits bifurcated from homoclinic orbit is also considered. |
Keywords： |
Local coordinate system, Homoclinic orbit, Bifurcation |
Classification： |
34C23, 34C37, 37C29 |
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