Centers and isochronous centers of a class of quasi-analytic switching systems
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Abstract 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 those 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.
Keywordsquasi-analytic switching systems Lyapunov constant limit cycle center isochronous center
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This work was supported by National Natural Science Foundation of China (Grant Nos. 11371373 and 11601212), Applied Mathematics Enhancement Program of Linyi University and the Natural Science and Engineering Research Council of Canada (Grant No. R2686A02).
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