Centers and isochronous centers of a class of quasi-analytic switching systems

作者：Li, Feng; Yu, Pei^*; Liu, Yirong; Liu, Yuanyuan

来源：Science China Mathematics, 2018, 61(7): 1201-1218.

DOI：10.1007/s11425-016-9158-2

• quasi-analytic switching systems
• Lyapunov constant
• limit cycle
• center
• isochronous center

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.

• 出版日期2018-7
• 单位中南大学