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Qualitative Theory of Dynamical Systems

, Volume 18, Issue 3, pp 841–871 | Cite as

Planar Semi-quasi Homogeneous Polynomial Differential Systems with a Given Degree

  • Yuzhou Tian
  • Haihua LiangEmail author
Article
  • 86 Downloads

Abstract

This paper study the planar semi-quasi homogeneous polynomial differential systems (PSQHPDS), which can be regarded as a generalization of semi-homogeneous and of quasi-homogeneous systems. By using the algebraic skills, several important properties of PSQHPDS are derived and are employed to establish an algorithm for obtaining all the explicit expressions of PSQHPDS with a given degree. As an application of this algorithm, we research the center problem of quadratic and cubic PSQHPDS. The nonexistence of the quadratic center is proved and the canonical form of cubic center is found.

Keywords

Semi-quasi homogeneous Polynomial differential systems Algorithm Center 

Mathematics Subject Classification

Primary 37C10 Secondary 34C25 Tertiary 68W99 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Systems ScienceGuangdong Polytechnic Normal UniversityGuangzhouPeople’s Republic of China
  2. 2.School of Mathematics (Zhuhai)Sun Yat-sen UniversityZhuhaiPeople’s Republic of China

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