Periodic solutions with equal period for the Friedmann-Robertson-Walker model (Q1691038)

In this paper, the authors study the periodic solutions of the equation of barotropic Friedmann-Robertson-Walker cosmologies having the form \[ aa''+\gamma (a')^2+\gamma k=\frac{1}{3}\Lambda (\gamma +1) a^2, \] where all the letters except \(a\) are parameters. By using variable transformation, the authors convert the original second order ordinary differential equation into a planar dynamical system, and then they prove that the latter has two isochronous centers under certain parameter conditions. Consequently, two families of periodic solutions with equal period for the system are found.