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| PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE-LOOP |
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Citation： |
ZHAO Yulin,WU Xiaoming,ZHU Siming.PERTURBATIONS OF A KIND OF DEGENERATE QUADRATIC HAMILTONIAN SYSTEM WITH SADDLE-LOOP[J].Chinese Annals of Mathematics B,2002,23(1):85~94 |
| Page view： 1198
Net amount： 990 |
Authors： |
ZHAO Yulin; WU Xiaoming;ZHU Siming |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10101031, No. 10071097), Guangdong Natural Science Foundation (No. 001289) and the Foundation of Zhongshan Unversity for Younger Teacher. |
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| Abstract： |
The authors investigate a kind of degenerate quadratic Hamiltonian systems with saddle-loop. Under quadratic perturbations, it is proved that the perturbed system has at most two limit cycles in the nite plane. The proof relies on a careful analysis of a related Abelian integral. |
Keywords： |
Limit cycles, Quadratic systems, Abelian integrals |
Classification： |
34C05, 34C07 |
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