Solution of center-focus problem for a class of cubic systems

Abstract

For a class of cubic systems, the authors give a representation of the nth 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.

Keywords

Center variety / Isochronous center / Center conditions / Integrating factor

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