# American Institute of Mathematical Sciences

July  2016, 36(7): 4015-4025. doi: 10.3934/dcds.2016.36.4015

## Planar quasi-homogeneous polynomial systems with a given weight degree

 1 School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China 2 Department of Mathematics, Shanghai Normal University, Shanghai 200234

Received  January 2015 Revised  January 2016 Published  March 2016

In this paper, we investigate a class of quasi-homogeneous polynomial systems with a given weight degree. Firstly, by some analytical skills, several properties about this kind of systems are derived and an algorithm can be established to obtain all possible explicit systems for a given weight degree. Then, we focus on center problems for such systems and provide some necessary conditions for the existence of centers. Finally, for a specific quasi-homogeneous polynomial system, we characterize its center and prove that the center is not isochronous.
Citation: Yanqin Xiong, Maoan Han. Planar quasi-homogeneous polynomial systems with a given weight degree. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 4015-4025. doi: 10.3934/dcds.2016.36.4015
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