On the focus order of planar polynomial differential equations

Yu Qiu Department of Mathematics, Peking University, Beijing 100871, China Jiazhong Yang Partially supported by NSCF No. 10571002 and No. 10871006 of China.

Number Theory mathscidoc:2206.24005

Journal of Differential Equations, 246, (8), 3361-3379, 2009.4
This paper is devoted to finding the highest possible focus order of planar polynomial differential equations. The results consist of two parts: (i) we explicitly construct a class of concrete systems of degree n, where n+1 is a prime p or a power of a prime p^k, and show that these systems can have a focus order n^2-n; (ii) we theoretically prove the existence of polynomial systems of degree n having a focus order n^2-1 for any even number n. Corresponding results for odd n and more concrete examples having higher focus orders are given too.
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@inproceedings{yu2009on,
  title={On the focus order of planar polynomial differential equations},
  author={Yu Qiu, and Jiazhong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626163543142745459},
  booktitle={Journal of Differential Equations},
  volume={246},
  number={8},
  pages={3361-3379},
  year={2009},
}
Yu Qiu, and Jiazhong Yang. On the focus order of planar polynomial differential equations. 2009. Vol. 246. In Journal of Differential Equations. pp.3361-3379. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626163543142745459.
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