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Finite Cyclicity of Some Graphics Through a Nilpotent Point of Saddle Type Inside Quadratic Systems

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Abstract

In this paper we show the finite cyclicity of the two graphics \((I_{12}^1)\) and \((I_{13}^1)\) through a triple nilpotent point of saddle type inside quadratic vector fields. These results contribute to the program launched in 1994 by Dumortier, Roussarie and Rousseau (DRR program) to show the existence of a uniform upper bound for the number of limit cycles for planar quadratic vector fields.

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References

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Authors and Affiliations

  1. Department of Mathematics and Statistics and CRM, University of Montreal, Montreal, H3C 3J7, Canada

    Christiane Rousseau

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada

    Chunhua Shan

  3. Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

    Huaiping Zhu

Authors
  1. Christiane Rousseau
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  2. Chunhua Shan
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  3. Huaiping Zhu
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Correspondence to Huaiping Zhu.

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Rousseau, C., Shan, C. & Zhu, H. Finite Cyclicity of Some Graphics Through a Nilpotent Point of Saddle Type Inside Quadratic Systems. Qual. Theory Dyn. Syst. 15, 237–256 (2016). https://doi.org/10.1007/s12346-015-0143-2

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  • DOI: https://doi.org/10.1007/s12346-015-0143-2

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