Existence of random invariant periodic curves via random semiuniform ergodic theorem

Abstract

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 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].

References in corpus (4)

• Random Periodic Solutions of Random Dynamical Systems
• Pathwise Random Periodic Solutions of Stochastic Differential Equations
• Stationary Solutions of SPDEs and Infinite Horizon BDSDEs
• Random Periodic Solutions of SPDEs via Integral Equations and Wiener-Sobolev Compact Embedding

Cited by in corpus (2)

• Random periodic solutions and ergodicity for stochastic differential equations
• Averaging principle for stochastic differential equations in the random periodic regime