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# On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities

Published:2015-09-10
Printed: Dec 2015
• Jaume Llibre,
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
• Xiang Zhang,
Department of Mathematics, MOE-LSC, Shanghai Jiao tong University, Shanghai, 200240, P. R. China
 Format: LaTeX MathJax PDF

## Abstract

We consider the class of polynomial differential systems of the form $\dot x= \lambda x-y+P_n(x,y)$, $\dot y=x+\lambda y+ Q_n(x,y),$ where $P_n$ and $Q_n$ are homogeneous polynomials of degree $n$. For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.
 Keywords: polynomial differential system, limit cycles, differential equations on the cylinder
 MSC Classifications: 34C35 - unknown classification 34C3534D30 - Structural stability and analogous concepts [See also 37C20]

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