On the analytic commutator for $\Lambda$−$\Omega$ differential systems

Abstract

In this paper, we give the necessary and sufficient conditions for some $\Lambda$−$\Omega$ differential systems to have an analytic commutator, use these properties to judge the origin point of the $\Lambda$−$\Omega$ differential systems to be an isochronous center.

Keywords

• analytic commutator
• isochronous center
• $\lambda$−$\omega$ system
• center conditions