一类拟解析切换系统的中心与等距中心
Center and isochronous center of a class of quasi-analytic switching systems
摘要：
本文研究了一类二次拟解析切换系统的可积性和线性化问题。本文改进了现有的计算准解析开关系统的焦点值和周期常数的方法。特别地，通过证明二次拟解析切换系统在原点和无穷远处分别存在6个和7个极限环，证明了拟解析切换系统的动力学行为比连续拟解析切换系统的动力学行为更复杂.此外，还得到了系统中心和等距中心的判别条件。
英文摘要：
In this paper, we study the integrability and linearization of a class of quadratic quasi-analytic switching systems. We improve an existing method to compute the focus values and periodic constants of quasi-analytic switching systems. In particular, with our method, we demonstrate that the dynamical behaviors of quasi-analytic switching systems are more complex than that of continuous quasi-analytic systems, by showing the existence of six and seven limit cycles in the neighborhood of the origin and infinity, respectively, in a quadratic quasi-analytic switching system. Moreover, explicit conditions are obtained for classifying the centers and isochronous centers of the system.
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