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Cyclicity of planar homoclinic loops and quadratic integrable systems

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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.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiaotong University, 200030, Shanghai, China

    Maoan Han

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  1. Maoan Han
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Project supported by the National Natural Science Foundation of China.

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Han, M. Cyclicity of planar homoclinic loops and quadratic integrable systems. Sci. China Ser. A-Math. 40, 1247–1258 (1997). https://doi.org/10.1007/BF02876370

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  • DOI: https://doi.org/10.1007/BF02876370

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