arXiv 1609.080482016-09-26math.CA

On the number of limit cycles for a class of discontinuous quadratic differential systems

Xiuli Cen, Shimin Li, Yulin Zhao

英文摘要：

The present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center $\dot{x}=-y+\frac{16}{3}x^{2}-\frac{4}{3}y^{2},\dot{y}=x+\frac{8}{3}xy$ by the averaging method of first order, when it is perturbed inside a class of discontinuous quadratic polynomial differential systems. The \emph{Chebyshev criterion} is used to show that this maximum number is 5 and can be realizable. The result and that in paper \cite{LC} completely answer the questions left in the paper \cite{LM}.

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