Centers of discontinuous piecewise smooth quasi–homogeneous polynomial differential systems

Hebai Chen; Jaume Llibre; Yilei Tang

doi:10.3934/dcdsb.2019150

Article Contents

2019, Volume 24, Issue 12: 6495-6509. Doi: 10.3934/dcdsb.2019150

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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: November 30, 2018

Revised: December 31, 2018

Early access: July 2019

Published: September 2019

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Abstract

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.

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Mathematics Subject Classification: 37J35, 34A05, 34A34, 34C14.

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