### Abstract

We characterize the centers of the quasi-homogeneous planar polynomial differential systems of degree three. Such systems do not admit isochronous centers. At most one limit cycle can bifurcate from the periodic orbits of a center of a cubic homogeneous polynomial system using the averaging theory of first order. © 2013 Elsevier Inc.

Original language | English |
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Pages (from-to) | 233-250 |

Journal | Advances in Mathematics |

Volume | 254 |

DOIs | |

Publication status | Published - 20 Mar 2014 |

### Keywords

- Centers
- Limit cycles
- Quasi-homogeneous polynomial systems

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## Cite this

Aziz, W., Llibre, J., & Pantazi, C. (2014). Centers of quasi-homogeneous polynomial differential equations of degree three.

*Advances in Mathematics*,*254*, 233-250. https://doi.org/10.1016/j.aim.2013.12.006