Isochronous center conditions and limit cycles at infinity for a class of fifth systems

In this article,the center conditions,isochronous center conditions and bifurcation of limit cycles at infinity for a class of fifth system are investigated.Firstly,the first eight singular point quantities are computed and conditions for infinity to be a center are deduced as well,then a system that bifurcates eight limit cycles in the neighborhood of infinity are constructed.At the same time the new algorithm is applied to find necessary conditions for such isochronous center,then proofs of isochronicity of these systems by using some effective methods are given.