Center of planar quintic quasi--homogeneous polynomial differential systems

Yilei Tang; Long Wang; Xiang Zhang

doi:10.3934/dcds.2015.35.2177

Article Contents

2015, Volume 35, Issue 5: 2177-2191. Doi: 10.3934/dcds.2015.35.2177

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Center of planar quintic quasi--homogeneous polynomial differential systems

1.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240
2.
Department of Mathematics, Southern Polytechnic State University, Marietta, GA 30060
3.
Department of Mathematics and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240

Received: April 30, 2014

Revised: June 30, 2014

Published: May 2017

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Abstract

In this paper we first characterize all quasi--homogeneous but non--homogeneous planar polynomial differential systems of degree five, and then among which we classify all the ones having a center at the origin. Finally we present the topological phase portrait of the systems having a center at the origin.

Keywords:

Quasi--homogeneous quintic polynomial systems,
centers,
global phase portrait,
blow up,
generalized normal sectors.

Mathematics Subject Classification: Primary: 37G05; Secondary: 37G10, 34C23, 34C20.

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