Bi-center problem for some classes of Z2-equivariant systems
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摘要
We investigate the simultaneous existence of two centers and their isochronicity for two families of planar Z2-equivariant differential systems. First, for a family studied by Liu and Li (2011) we present the necessary and sufficient conditions for the existence of an isochronous bi-center. Next, we give conditions for the existence of a bi-center and study its isochronicity for a planar Z2-equivariant quintic system having two weak foci or centers. We also give two examples of non-Hamiltonian cubic systems with three isochronous centers.
论文关键词:Bi-centers,Isochronicity,Lyapunov constants,Z2-equivariant systems
论文评审过程:Received 23 July 2016, Revised 10 December 2016, Available online 13 February 2017, Version of Record 23 February 2017.
论文官网地址:https://doi.org/10.1016/j.cam.2017.02.003