For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a pa...For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a particular system are considered. They show that the system has a center at the origin if and only if the first seven Liapunov constants vanish, and cannot have an isochronous center at the origin.展开更多
基金supported by the National Natural Science Foundation of China(No.11401285)the Foundation for Research in Experimental Techniques of Liaocheng University(No.LDSY2014110)
文摘For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a particular system are considered. They show that the system has a center at the origin if and only if the first seven Liapunov constants vanish, and cannot have an isochronous center at the origin.
