Existence of random invariant periodic curves via random semiuniform ergodic theorem

We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system on a cylinder [Formula: see text] has a dissipative structure, we proved that a random invariant compact set can be expressed as a union of finite of number of random periodic curves. The idea in this paper is closely related to the work recently considered by Zhao and Zheng [46].