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Cyclicity of homoclinic loops and degenerate cubic Hamiltonians |
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| Authors: | Maoan Han Yanqian Ye and Deming Zhu |
| Institution: | (1) Department of Mathematics, Shanghai Jiaotong University, 200030 Shanghai, China;(2) Department of Mathematics, Nanjing University, 210008 Nanjing, China;(3) Department of Mathematics, East China Normal University, 200062 Shanghai, China |
| Abstract: | New conditions for a planar homoclinic loop to have cyclicity two under multiple parameter perturbations have been obtained. As an application it is proved that a homoclinic loop of a nongeneric cubic Hamiltonian has cyclicity two under arbitrary quadratic perturbations. Project supported by the National Natural Science Foundation of China (Grant Nos. 19531070 and 19771037). |
| Keywords: | homoclinic loop bifurcation cyclicity quadratic system |
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