Cyclicity of planar homoclinic loops and quadratic integrable systems |
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Authors: | Maoan Han |
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Institution: | (1) Department of Mathematics, Shanghai Jiaotong University, 200030 Shanghai, China |
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Abstract: | A general method for a homoclinic loop of planar Hamiltonian systems to bifurcate two or three limit cycles under perturbations
is established. Certain conditions are given under which the cyclicity of a homoclinic loop equals 1 or 2. As an application
to quadratic systems, it is proved that the cyclicity of homoclinic loops of quadratic integrable and non-Hamiltonian systems
equals 2 except for one case.
Project supported by the National Natural Science Foundation of China. |
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Keywords: | homoclinic loop bifurcation limit cycle cyclicity |
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