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## Centers of discontinuous piecewise smooth quasi–homogeneous polynomial differential systems

 a. School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China b. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350108, China c. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain d. School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China

Received  December 2018 Revised  January 2019 Published  July 2019

In this paper we investigate the center problem for the discontinuous piecewise smooth quasi–homogeneous but non–homogeneous polynomial differential systems. First, we provide sufficient and necessary conditions for the existence of a center in the discontinuous piecewise smooth quasi–homogeneous polynomial differential systems. Moreover, these centers are global, and the period function of their periodic orbits is monotonic. Second, we characterize the centers of the discontinuous piecewise smooth quasi–homogeneous cubic and quartic polynomial differential systems.

Citation: Hebai Chen, Jaume Llibre, Yilei Tang. Centers of discontinuous piecewise smooth quasi–homogeneous polynomial differential systems. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2019150
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Positive (or negative) Poincaré half-return map
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