Random attractors for dissipative systems with rough noises

<p style='text-indent:20px;'>We provide an analytic approach to study the asymptotic dynamics of rough differential equations, with driving noises Hölder continuity. Such systems can be solved Lyons' theory paths, in particular integrals are understood Gubinelli sense for controlled paths. Using framework random dynamical and attractors, we prove existence upper semi-continuity global pullback attractor dissipative perturbed by bounded noises. Moreover, if unperturbed system is strictly then a singleton sufficiently small noise intensity.</p>