Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems

Christiane Rousseau; Chunhua Shan; Huaiping Zhu

Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems

Classical Analysis and ODEs 2015-02-04 v1 Dynamical Systems

Authors: Christiane Rousseau , Chunhua Shan , Huaiping Zhu

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.

Keywords

finite cyclicity quadratic vector fields nilpotent point saddle type limit cycles graphics DRR program

Cite

@article{arxiv.1502.00689,
  title  = {Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems},
  author = {Christiane Rousseau and Chunhua Shan and Huaiping Zhu},
  journal= {arXiv preprint arXiv:1502.00689},
  year   = {2015}
}

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18 pages, 7 figures

Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems

Abstract

Keywords

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