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Cyclicity of homoclinic loops and degenerate cubic Hamiltonians

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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.

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Authors and Affiliations

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

    Han Maoan

  2. Department of Mathematics, Nanjing University, 210008, Nanjing, China

    Ye Yanqian

  3. Department of Mathematics, East China Normal University, 200062, Shanghai, China

    Zhu Deming

Authors
  1. Han Maoan
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  2. Ye Yanqian
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  3. Zhu Deming
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Additional information

Project supported by the National Natural Science Foundation of China (Grant Nos. 19531070 and 19771037).

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Maoan, H., Yanqian, Y. & Deming, Z. Cyclicity of homoclinic loops and degenerate cubic Hamiltonians. Sci. China Ser. A-Math. 42, 605–617 (1999). https://doi.org/10.1007/BF02880079

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  • DOI: https://doi.org/10.1007/BF02880079

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